API reference

CvStruct

class CvStruct(*args)

GetFEM CvStruct object

General constructor for CvStruct objects

basic_structure()

Get the simplest convex structure.

For example, the ‘basic structure’ of the 6-node triangle, is the canonical 3-noded triangle.

char()
Output a string description of the CvStruct.
dim()
Get the dimension of the convex structure.
display()
displays a short summary for a CvStruct object.
face(F)
Return the convex structure of the face F.
facepts(F)
Return the list of point indices for the face F.
nbpts()
Get the number of points of the convex structure.

Eltm

class Eltm(*args)

GetFEM Eltm object

This object represents a type of elementary matrix. In order to obtain a numerical value of theses matrices, see MeshIm.eltm().

If you have very particular assembling needs, or if you just want to check the content of an elementary matrix, this function might be useful. But the generic assembly abilities of gf_asm(...) should suit most needs.

General constructor for Eltm objects

  • E = Eltm('base', Fem FEM) return a descriptor for the integration of shape functions on elements, using the Fem FEM.
  • E = Eltm('grad', Fem FEM) return a descriptor for the integration of the gradient of shape functions on elements, using the Fem FEM.
  • E = Eltm('hessian', Fem FEM) return a descriptor for the integration of the hessian of shape functions on elements, using the Fem FEM.
  • E = Eltm('normal') return a descriptor for the unit normal of convex faces.
  • E = Eltm('grad_geotrans') return a descriptor to the gradient matrix of the geometric transformation.
  • E = Eltm('grad_geotrans_inv') return a descriptor to the inverse of the gradient matrix of the geometric transformation (this is rarely used).
  • E = Eltm('product', Eltm A, Eltm B) return a descriptor for the integration of the tensorial product of elementary matrices A and B.

Fem

class Fem(*args)

GetFEM Fem object

This object represents a finite element method on a reference element.

General constructor for Fem objects

  • F = Fem('interpolated_fem', MeshFem mf, MeshIm mim, [ivec blocked_dof]) Build a special Fem which is interpolated from another MeshFem.

    Using this special finite element, it is possible to interpolate a given MeshFem mf on another mesh, given the integration method mim that will be used on this mesh.

    Note that this finite element may be quite slow, and eats much memory.

  • F = Fem(string fem_name) The fem_name should contain a description of the finite element method. Please refer to the getfem++ manual (especially the description of finite element and integration methods) for a complete reference. Here is a list of some of them:

    • FEM_PK(n,k) : classical Lagrange element Pk on a simplex of dimension n.
    • FEM_PK_DISCONTINUOUS(n,k[,alpha]) : discontinuous Lagrange element Pk on a simplex of dimension n.
    • FEM_QK(n,k) : classical Lagrange element Qk on quadrangles, hexahedrons etc.
    • FEM_QK_DISCONTINUOUS(n,k[,alpha]) : discontinuous Lagrange element Qk on quadrangles, hexahedrons etc.
    • FEM_Q2_INCOMPLETE : incomplete 2D Q2 element with 8 dof (serendipity Quad 8 element).
    • FEM_PK_PRISM(n,k) : classical Lagrange element Pk on a prism of dimension n.
    • FEM_PK_PRISM_DISCONTINUOUS(n,k[,alpha]) : classical discontinuous Lagrange element Pk on a prism.
    • FEM_PK_WITH_CUBIC_BUBBLE(n,k) : classical Lagrange element Pk on a simplex with an additional volumic bubble function.
    • FEM_P1_NONCONFORMING : non-conforming P1 method on a triangle.
    • FEM_P1_BUBBLE_FACE(n) : P1 method on a simplex with an additional bubble function on face 0.
    • FEM_P1_BUBBLE_FACE_LAG : P1 method on a simplex with an additional lagrange dof on face 0.
    • FEM_PK_HIERARCHICAL(n,k) : PK element with a hierarchical basis.
    • FEM_QK_HIERARCHICAL(n,k) : QK element with a hierarchical basis
    • FEM_PK_PRISM_HIERARCHICAL(n,k) : PK element on a prism with a hierarchical basis.
    • FEM_STRUCTURED_COMPOSITE(Fem f,k) : Composite Fem f on a grid with k divisions.
    • FEM_PK_HIERARCHICAL_COMPOSITE(n,k,s) : Pk composite element on a grid with s subdivisions and with a hierarchical basis.
    • FEM_PK_FULL_HIERARCHICAL_COMPOSITE(n,k,s) : Pk composite element with s subdivisions and a hierarchical basis on both degree and subdivision.
    • FEM_PRODUCT(A,B) : tensorial product of two polynomial elements.
    • FEM_HERMITE(n) : Hermite element P3 on a simplex of dimension n = 1, 2, 3.
    • FEM_ARGYRIS : Argyris element P5 on the triangle.
    • FEM_HCT_TRIANGLE : Hsieh-Clough-Tocher element on the triangle (composite P3 element which is C1), should be used with IM_HCT_COMPOSITE() integration method.
    • FEM_QUADC1_COMPOSITE : Quadrilateral element, composite P3 element and C1 (16 dof).
    • FEM_REDUCED_QUADC1_COMPOSITE : Quadrilateral element, composite P3 element and C1 (12 dof).
    • FEM_RT0(n) : Raviart-Thomas element of order 0 on a simplex of dimension n.
    • FEM_NEDELEC(n) : Nedelec edge element of order 0 on a simplex of dimension n.

    Of course, you have to ensure that the selected fem is compatible with the geometric transformation: a Pk fem has no meaning on a quadrangle.

base_value(p)

Evaluate all basis functions of the FEM at point p.

p is supposed to be in the reference convex!

char()

Ouput a (unique) string representation of the Fem.

This can be used to perform comparisons between two different Fem objects.

dim()
Return the dimension (dimension of the reference convex) of the Fem.
display()
displays a short summary for a Fem object.
estimated_degree()

Return an estimation of the polynomial degree of the Fem.

This is an estimation for fem which are not polynomials.

grad_base_value(p)

Evaluate the gradient of all base functions of the Fem at point p.

p is supposed to be in the reference convex!

hess_base_value(p)

Evaluate the Hessian of all base functions of the Fem at point p.

p is supposed to be in the reference convex!.

is_equivalent()

Return 0 if the Fem is not equivalent.

Equivalent Fem are evaluated on the reference convex. This is the case of most classical Fem’s.

is_lagrange()
Return 0 if the Fem is not of Lagrange type.
is_polynomial()
Return 0 if the basis functions are not polynomials.
nbdof(cv=None)

Return the number of dof for the Fem.

Some specific Fem (for example ‘interpolated_fem’) may require a convex number cv to give their result. In most of the case, you can omit this convex number.

poly_str()

Return the polynomial expressions of its basis functions in the reference convex.

The result is expressed as a tuple of strings. Of course this will fail on non-polynomial Fem’s.

pts(cv=None)

Get the location of the dof on the reference element.

Some specific Fem may require a convex number cv to give their result (for example ‘interpolated_fem’). In most of the case, you can omit this convex number.

target_dim()

Return the dimension of the target space.

The target space dimension is usually 1, except for vector Fem.

GeoTrans

class GeoTrans(*args)

GetFEM GeoTrans object

The geometric transformation must be used when you are building a custom mesh convex by convex (see the add_convex() function of Mesh): it also defines the kind of convex (triangle, hexahedron, prism, etc..)

General constructor for GeoTrans objects

  • GT = GeoTrans(string name) The name argument contains the specification of the geometric transformation as a string, which may be:

    • GT_PK(n,k) : Transformation on simplexes, dim n, degree k.
    • GT_QK(n,k) : Transformation on parallelepipeds, dim n, degree k.
    • GT_PRISM(n,k) : Transformation on prisms, dim n, degree k.
    • GT_PRODUCT(A,B) : Tensorial product of two transformations.
    • GT_LINEAR_PRODUCT(GeoTrans gt1,GeoTrans gt2) : Linear tensorial product of two transformations
char()

Output a (unique) string representation of the GeoTrans.

This can be used to perform comparisons between two different GeoTrans objects.

dim()

Get the dimension of the GeoTrans.

This is the dimension of the source space, i.e. the dimension of the reference convex.

display()
displays a short summary for a GeoTrans object.
is_linear()
Return 0 if the GeoTrans is not linear.
nbpts()
Return the number of points of the GeoTrans.
normals()

Get the normals for each face of the reference convex of the GeoTrans.

The normals are stored in the columns of the output matrix.

pts()

Return the reference convex points of the GeoTrans.

The points are stored in the columns of the output matrix.

transform(G, Pr)

Apply the GeoTrans to a set of points.

G is the set of vertices of the real convex, Pr is the set of points (in the reference convex) that are to be transformed. The corresponding set of points in the real convex is returned.

GlobalFunction

class GlobalFunction(*args)

GetFEM GlobalFunction object

Global function object is represented by three functions:

  • The function val.
  • The function gradient grad.
  • The function Hessian hess.

this type of function is used as local and global enrichment function. The global function Hessian is an optional parameter (only for fourth order derivative problems).

General constructor for GlobalFunction objects

  • GF = GlobalFunction('cutoff', int fn, scalar r, scalar r1, scalar r0) Create a cutoff global function.
  • GF = GlobalFunction('crack', int fn) Create a near-tip asymptotic global function for modelling cracks.
  • GF = GlobalFunction('parser', string val[, string grad[, string hess]]) Create a global function from strings val, grad and hess.
  • GF = GlobalFunction('product', GlobalFunction F, GlobalFunction G) Create a product of two global functions.
  • GF = GlobalFunction('add', GlobalFunction gf1, GlobalFunction gf2) Create a add of two global functions.
char()

Output a (unique) string representation of the GlobalFunction.

This can be used to perform comparisons between two different GlobalFunction objects. This function is to be completed.

display()
displays a short summary for a GlobalFunction object.
grad(PTs)

Return grad function evaluation in PTs (column points).

On return, each column of GRADs is of the form [Gx,Gy].

hess(PTs)

Return hess function evaluation in PTs (column points).

On return, each column of HESSs is of the form [Hxx,Hxy,Hyx,Hyy].

val(PTs)
Return val function evaluation in PTs (column points).

Integ

class Integ(*args)

GetFEM Integ object

General object for obtaining handles to various integrations methods on convexes (used when the elementary matrices are built).

General constructor for Integ objects

  • I = Integ(string method) Here is a list of some integration methods defined in getfem++ (see the description of finite element and integration methods for a complete reference):

    • IM_EXACT_SIMPLEX(n) : Exact integration on simplices (works only with linear geometric transformations and PK Fem’s).
    • IM_PRODUCT(A,B) : Product of two integration methods.
    • IM_EXACT_PARALLELEPIPED(n) : Exact integration on parallelepipeds.
    • IM_EXACT_PRISM(n) : Exact integration on prisms.
    • IM_GAUSS1D(k) : Gauss method on the segment, order k=1,3,...,99.
    • IM_NC(n,k) : Newton-Cotes approximative integration on simplexes, order k.
    • IM_NC_PARALLELEPIPED(n,k) : Product of Newton-Cotes integration on parallelepipeds.
    • IM_NC_PRISM(n,k) : Product of Newton-Cotes integration on prisms.
    • IM_GAUSS_PARALLELEPIPED(n,k) : Product of Gauss1D integration on parallelepipeds.
    • IM_TRIANGLE(k) : Gauss methods on triangles k=1,3,5,6,7,8,9,10,13,17,19.
    • IM_QUAD(k) : Gauss methods on quadrilaterons k=2,3,5, ...,17. Note that IM_GAUSS_PARALLELEPIPED should be prefered for QK Fem’s.
    • IM_TETRAHEDRON(k) : Gauss methods on tetrahedrons k=1,2,3,5,6 or 8.
    • IM_SIMPLEX4D(3) : Gauss method on a 4-dimensional simplex.
    • IM_STRUCTURED_COMPOSITE(im,k) : Composite method on a grid with k divisions.
    • IM_HCT_COMPOSITE(im) : Composite integration suited to the HCT composite finite element.

    Example:

    • I = Integ(‘IM_PRODUCT(IM_GAUSS1D(5),IM_GAUSS1D(5))’)

    is the same as:

    • I = Integ(‘IM_GAUSS_PARALLELEPIPED(2,5)’)

    Note that ‘exact integration’ should be avoided in general, since they only apply to linear geometric transformations, are quite slow, and subject to numerical stability problems for high degree Fem’s.

char()

Ouput a (unique) string representation of the integration method.

This can be used to comparisons between two different Integ objects.

coeffs()

Returns the coefficients associated to each integration point.

Only for approximate methods, this has no meaning for exact integration methods!

dim()
Return the dimension of the reference convex of the method.
display()
displays a short summary for a Integ object.
face_coeffs(F)

Returns the coefficients associated to each integration of a face.

Only for approximate methods, this has no meaning for exact integration methods!

face_pts(F)

Return the list of integration points for a face.

Only for approximate methods, this has no meaning for exact integration methods!

is_exact()
Return 0 if the integration is an approximate one.
nbpts()

Return the total number of integration points.

Count the points for the volume integration, and points for surface integration on each face of the reference convex.<Par>

Only for approximate methods, this has no meaning for exact integration methods!

pts()

Return the list of integration points

Only for approximate methods, this has no meaning for exact integration methods!

LevelSet

class LevelSet(*args)

GetFEM LevelSet object

The level-set object is represented by a primary level-set and optionally a secondary level-set used to represent fractures (if p(x) is the primary level-set function and s(x) is the secondary level-set, the crack is defined by p(x)=0 and s(x)<=0: the role of the secondary is to determine the crack front/tip).

Note

All tools listed below need the package qhull installed on your system. This package is widely available. It computes convex hull and delaunay triangulations in arbitrary dimension.

General constructor for LevelSet objects

  • LS = LevelSet(Mesh m, int d[, string 'ws'| string f1[, string f2 | string 'ws']]) Create a LevelSet object on a Mesh represented by a primary function (and optional secondary function, both) defined on a lagrange MeshFem of degree d.

    If ws (with secondary) is set; this levelset is represented by a primary function and a secondary function. If f1 is set; the primary function is defined by that expression. If f2 is set; this levelset is represented by a primary function and a secondary function defined by these expressions.

char()

Output a (unique) string representation of the LevelSet.

This can be used to perform comparisons between two different LevelSet objects. This function is to be completed.

degree()
Return the degree of lagrange representation.
display()
displays a short summary for a LevelSet.
memsize()
Return the amount of memory (in bytes) used by the level-set.
mf()
Return a reference on the MeshFem object.
set_values(*args)

Synopsis: LevelSet.set_values(self, {mat v1|string func_1}[, mat v2|string func_2])

Set values of the vector of dof for the level-set functions.

Set the primary function with the vector of dof v1 (or the expression func_1) and the secondary function (if any) with the vector of dof v2 (or the expression func_2)

simplify(eps=0.01)
Simplify dof of level-set optionally with the parameter eps.
values(nls)

Return the vector of dof for nls funtion.

If nls is 0, the method return the vector of dof for the primary level-set funtion. If nls is 1, the method return the vector of dof for the secondary level-set function (if any).

MdBrick

class MdBrick(*args)

GetFEM MdBrick object

General constructor for MdBrick objects

  • B = MdBrick('constraint', MdBrick pb, string CTYPE[, int nfem]) Build a generic constraint brick.

    It may be useful in some situations, such as the Stokes problem where the pressure is defined modulo a constant. In such a situation, this brick can be used to add an additional constraint on the pressure value. CTYPE has to be chosen among ‘augmented’, ‘penalized’, and ‘eliminated’. The constraint can be specified with MdBrick.constraints(). Note that Dirichlet bricks (except the ‘generalized Dirichlet’ one) are also specializations of the ‘constraint’ brick.

  • B = MdBrick('dirichlet', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem]) Build a Dirichlet condition brick which impose the value of a field along a mesh boundary.

    The bnum parameter selects on which mesh region the Dirichlet condition is imposed. CTYPE has to be chosen among ‘augmented’, ‘penalized’, and ‘eliminated’. The mf_m may generally be taken as the MeshFem of the unknown, but for ‘augmented’ Dirichlet conditions, you may have to respect the Inf-Sup condition and choose an adequate MeshFem.

  • B = MdBrick('dirichlet on normal component', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem]) Build a Dirichlet condition brick which imposes the value of the normal component of a vector field.

  • B = MdBrick('dirichlet on normal derivative', MdBrick pb, int bnum, MeshFem mf_m, string CTYPE[, int nfem]) Build a Dirichlet condition brick which imposes the value of the normal derivative of the unknown.

  • B = MdBrick('generalized dirichlet', MdBrick pb, int bnum[, int nfem]) This is the “old” Dirichlet brick of getfem.

    This brick can be used to impose general Dirichlet conditions h(x)u(x) = r(x), however it may have some issues with elaborated Fem’s (such as Argyris, etc). It should be avoided when possible.

  • B = MdBrick('source term', MdBrick pb[, int bnum=-1[, int nfem]]) Add a boundary or volumic source term ( int B.v ).

    If bnum is omitted (or set to -1) , the brick adds a volumic source term on the whole mesh. For bnum >= 0, the source term is imposed on the mesh region bnum. Use MdBrick.set_param(‘source term’,mf,B) to set the source term field. The source term is expected as a vector field of size Q (with Q = qdim).

  • B = MdBrick('normal source term', MdBrick pb, int bnum[, int nfem]) Add a boundary source term ( int (Bn).v ).

    The source term is imposed on the mesh region bnum (which of course is not allowed to be a volumic region, only boundary regions are allowed). Use MdBrick.set_param(‘source term’,mf,B) to set the source term field. The source term B is expected as tensor field of size QxN (with Q = qdim, N = mesh dim). For example, if you consider an elasticity problem, this brick may be used to impose a force on the boundary with B as the stress tensor.

  • B = MdBrick('normal derivative source term', MdBrick parent, int bnum[, int nfem]) Add a boundary source term ( int (partial_n B).v ).

    The source term is imposed on the mesh region bnum. Use MdBrick.set_param(‘source term’,mf,B) to set the source term field, which is expected as a vector field of size Q (with Q = qdim).

  • B = MdBrick('neumann KirchhoffLove source term', MdBrick pb, int bnum[, int nfem]) Add a boundary source term for neumann Kirchhoff-Love plate problems.

    Should be used with the Kirchhoff-Love flavour of the bilaplacian brick.

  • B = MdBrick('qu term', MdBrick pb[, int bnum[, int nfem]]) Update the tangent matrix with a int (Qu).v term.

    The Q(x) parameter is a matrix field of size qdim x qdim. An example of use is for the “iku” part of Robin boundary conditions partial_n u + iku = ...

  • B = MdBrick('mass matrix', MeshIm mim, MeshFem mf_u[, 'real'|'complex']) Build a mass-matrix brick.

  • B = MdBrick('generic elliptic', MeshIm mim, MeshFem mfu[, 'scalar'|'matrix'|'tensor'][, 'real'|'complex']) Setup a generic elliptic problem.

    a(x)*grad(U).grad(V)

    The brick parameter a may be a scalar field, a matrix field, or a tensor field (default is scalar).

  • B = MdBrick('helmholtz', MeshIm mim, MeshFem mfu[, 'real'|'complex']) Setup a Helmholtz problem.

    The brick has one parameter, ‘wave_number’.

  • B = MdBrick('isotropic linearized elasticity', MeshIm mim, MeshFem mfu) Setup a linear elasticity problem.

    The brick has two scalar parameter, ‘lambda’ and ‘mu’ (the Lame coefficients).

  • B = MdBrick('linear incompressibility term', MdBrick pb, MeshFem mfp[, int nfem]) Add an incompressibily constraint (div u = 0).

  • B = MdBrick('nonlinear elasticity', MeshIm mim, MeshFem mfu, string law) Setup a nonlinear elasticity (large deformations) problem.

    The material law can be chosen among:

    • ‘SaintVenant Kirchhoff’ : Linearized material law.
    • ‘Mooney Rivlin’ : To be used with the nonlinear incompressibily term.
    • ‘Ciarlet Geymonat’
  • B = MdBrick('nonlinear elasticity incompressibility term', MdBrick pb, MeshFem mfp[, int nfem]) Add an incompressibily constraint to a large strain elasticity problem.

  • B = MdBrick('small deformations plasticity', MeshIm mim, MeshFem mfu, scalar THRESHOLD) Setup a plasticity problem (with small deformations).

    The THRESHOLD parameter is the maximum value of the Von Mises stress before ‘plastification’ of the material.

  • B = MdBrick('dynamic', MdBrick pb, scalar rho[, int numfem]) Dynamic brick. This brick is not fully working.

  • B = MdBrick('bilaplacian', MeshIm mim, MeshFem mfu[, 'Kirchhoff-Love']) Setup a bilaplacian problem.

    If the ‘Kirchhoff-Love’ option is specified, the Kirchhoff-Love plate model is used.

  • B = MdBrick('navier stokes', MeshIm mim, MeshFem mfu, MeshFem mfp) Setup a Navier-Stokes problem (this brick is not ready, do not use it).

  • B = MdBrick('isotropic_linearized_plate', MeshIm mim, MeshIm mims, MeshFem mfut, MeshFem mfu3, MeshFem mftheta, scalar eps) Setup a linear plate model brick.

    For moderately thick plates, using the Reissner-Mindlin model. eps is the plate thinkness, the MeshFem mfut and mfu3 are used respectively for the membrane displacement and the transverse displacement of the plate. The MeshFem mftheta is the rotation of the normal (“section rotations”).

    The second integration method mims can be chosen equal to mim, or different if you want to perform sub-integration on the transverse shear term (mitc4 projection).

    This brick has two parameters “lambda” and “mu” (the Lame coefficients)

  • B = MdBrick('mixed_isotropic_linearized_plate', MeshIm mim, MeshFem mfut, MeshFem mfu3, MeshFem mftheta, scalar eps) Setup a mixed linear plate model brick.

    For thin plates, using Kirchhoff-Love model. For a non-mixed version, use the bilaplacian brick.

  • B = MdBrick('plate_source_term', MdBrick pb[, int bnum=-1[, int nfem]]) Add a boundary or a volumic source term to a plate problem.

    This brick has two parameters: “B” is the displacement (ut and u3) source term, “M” is the moment source term (i.e. the source term on the rotation of the normal).

  • B = MdBrick('plate_simple_support', MdBrick pb, int bnum, string CTYPE[, int nfem]) Add a “simple support” boundary condition to a plate problem.

    Homogeneous Dirichlet condition on the displacement, free rotation. CTYPE specifies how the constraint is enforced (‘penalized’, ‘augmented’ or ‘eliminated’).

  • B = MdBrick('plate_clamped_support', MdBrick pb, int bnum, string CTYPE[, int nfem]) Add a “clamped support” boundary condition to a plate problem.

    Homogeneous Dirichlet condition on the displacement and on the rotation. CTYPE specifies how the constraint is enforced (‘penalized’, ‘augmented’ or ‘eliminated’).

  • B = MdBrick('plate_closing', MdBrick pb[, int nfem]) Add a free edges condition for the mixed plate model brick.

    This brick is required when the mixed linearized plate brick is used. It must be inserted after all other boundary conditions (the reason is that the brick has to inspect all other boundary conditions to determine the number of disconnected boundary parts which are free edges).

char()

Output a (unique) string representation of the MdBrick.

This can be used to perform comparisons between two different MdBrick objects. This function is to be completed.

constraints(H, R)

Set the constraints imposed by a constraint brick.

This is only applicable to the bricks which inherit from the constraint brick, such as the Dirichlet ones. Imposes H.U=R.

constraints_rhs(H, R)

Set the right hand side of the constraints imposed by a constraint brick.

This is only applicable to the bricks which inherit from the constraint brick, such as the Dirichlet ones.

dim()
Get the dimension of the main mesh (2 for a 2D mesh, etc).
display()
displays a short summary for a MdBrick.
is_coercive()
Return true if the problem is coercive.
is_complex()
Return true if the problem uses complex numbers.
is_linear()
Return true if the problem is linear.
is_symmetric()
Return true if the problem is symmetric.
memsize()
Return the amount of memory (in bytes) used by the model brick.
mixed_variables()
Identify the indices of mixed variables (typically the pressure, etc.) in the tangent matrix.
nb_constraints()

Get the total number of dof constraints of the current problem.

This is the sum of the brick specific dof constraints plus the dof constraints of the parent bricks.

nbdof()

Get the total number of dof of the current problem.

This is the sum of the brick specific dof plus the dof of the parent bricks.

param(parameter_name)

Get the parameter value.

When the parameter has been assigned a specific MeshFem, it is returned as a large array (the last dimension being the MeshFem dof). When no MeshFem has been assigned, the parameter is considered to be constant over the mesh.

param_list()

Get the list of parameters names.

Each brick embeds a number of parameters (the Lame coefficients for the linearized elasticity brick, the wave number for the Helmholtz brick,...), described as a (scalar, or vector, tensor etc) field on a mesh_fem. You can read/change the parameter values with MdBrick.param() and MdBrick.param().

penalization_epsilon(eps)

Change the penalization coefficient of a constraint brick.

This is only applicable to the bricks which inherit from the constraint brick, such as the Dirichlet ones. And of course it is not effective when the constraint is enforced via direct elimination or via Lagrange multipliers. The default value of eps is 1e-9.

set_param(name, *args)

Synopsis: MdBrick.set_param(self, string name, {MeshFem mf,V | V})

Change the value of a brick parameter.

name is the name of the parameter. V should contain the new parameter value (vector or float). If a MeshFem is given, V should hold the field values over that MeshFem (i.e. its last dimension should be MeshFem.nbdof() or 1 for constant field).

solve(mds, *args)

Synopsis: MdBrick.solve(self,MdState mds[,...])

Run the standard getfem solver.

Note that you should be able to use your own solver if you want (it is possible to obtain the tangent matrix and its right hand side with the MdState.tangent_matrix() etc.).

Various options can be specified:

  • ‘noisy’ or ‘very noisy’

    the solver will display some information showing the progress (residual values etc.).

  • ‘max_iter’, NIT

    set the maximum iterations numbers.

  • ‘max_res’, RES

    set the target residual value.

  • ‘lsolver’, SOLVERNAME

    select explicitely the solver used for the linear systems (the default value is ‘auto’, which lets getfem choose itself). Possible values are ‘superlu’, ‘mumps’ (if supported), ‘cg/ildlt’, ‘gmres/ilu’ and ‘gmres/ilut’.

subclass()
Get the typename of the brick.
tresca(mds, mft)

Compute the Tresca stress criterion on the MeshFem mft.

Only available on bricks where it has a meaning: linearized elasticity, plasticity, nonlinear elasticity.

von_mises(mds, mfvm)

Compute the Von Mises stress on the MeshFem mfvm.

Only available on bricks where it has a meaning: linearized elasticity, plasticity, nonlinear elasticity. Note that in 2D it is not the “real” Von Mises (which should take into account the ‘plane stress’ or ‘plane strain’ aspect), but a pure 2D Von Mises.

MdState

class MdState(*args)

GetFEM MdState object

A model state is an object which store the state data for a chain of model bricks. This includes the global tangent matrix, the right hand side and the constraints.

This object is now deprecated and replaced by the Model object.

There are two sorts of model states, the real and the complex models states.

General constructor for MdState objects

  • MDS = MdState('real') Build a model state for real unknowns.

  • MDS = MdState('complex') Build a model state for complex unknowns.

  • MDS = MdState(MdBrick B) Build a modelstate for the brick B.

    Selects the real or complex state from the complexity of B.

char()

Output a (unique) string representation of the MdState.

This can be used to perform comparisons between two different MdState objects. This function is to be completed.

clear()
Clear the model state.
compute_reduced_residual()
Compute the reduced residual from the residual and constraints.
compute_reduced_system()
Compute the reduced system from the tangent matrix and constraints.
compute_residual(B)
Compute the residual for the brick B.
compute_tangent_matrix(B)
Update the tangent matrix from the brick B.
constraints_matrix()
Return the constraints matrix stored in the model state.
constraints_nullspace()
Return the nullspace of the constraints matrix.
display()
displays a short summary for a MdState.
is_complex()
Return 0 is the model state is real, 1 if it is complex.
memsize()
Return the amount of memory (in bytes) used by the model state.
reduced_residual()
Return the residual on the reduced system.
reduced_tangent_matrix()
Return the reduced tangent matrix (i.e. the tangent matrix after elimination of the constraints).
residual()
Return the residual.
set_state(U)
Update the internal state with the vector U.
state()
Return the vector of unknowns, which contains the solution after MdBrick.solve().
tangent_matrix()
Return the tangent matrix stored in the model state.
unreduce(U)
Reinsert the constraint eliminated from the system.

Mesh

class Mesh(*args)

GetFEM Mesh object

This object is able to store any element in any dimension even if you mix elements with different dimensions.

General constructor for Mesh objects

  • M = Mesh('empty', int dim) Create a new empty mesh.

  • M = Mesh('cartesian', vec X[, vec Y[, vec Z,..]]) Build quickly a regular mesh of quadrangles, cubes, etc.

  • M = Mesh('triangles grid', vec X, vec Y) Build quickly a regular mesh of triangles.

    This is a very limited and somehow deprecated function (See also Mesh('ptND'), Mesh('regular simplices') and Mesh('cartesian')).

  • M = Mesh('regular simplices', vec X[, vec Y[, vec Z,...]]['degree', int k]['noised']) Mesh a n-dimensionnal parallelepipeded with simplices (triangles, tetrahedrons etc) .

    The optional degree may be used to build meshes with non linear geometric transformations.

  • M = Mesh('curved', Mesh m, vec F) Build a curved (n+1)-dimensions mesh from a n-dimensions mesh m.

    The points of the new mesh have one additional coordinate, given by the vector F. This can be used to obtain meshes for shells. m may be a MeshFem object, in that case its linked mesh will be used.

  • M = Mesh('prismatic', Mesh m, int nl) Extrude a prismatic Mesh M from a Mesh m.

    In the additional dimension there are nl layers of elements built from 0 to 1.

  • M = Mesh('pt2D', mat P, imat T[, int n]) Build a mesh from a 2D triangulation.

    Each column of P contains a point coordinate, and each column of T contains the point indices of a triangle. n is optional and is a zone number. If n is specified then only the zone number n is converted (in that case, T is expected to have 4 rows, the fourth containing these zone numbers).

  • M = Mesh('ptND', mat P, imat T) Build a mesh from a n-dimensional “triangulation”.

    Similar function to ‘pt2D’, for building simplexes meshes from a triangulation given in T, and a list of points given in P. The dimension of the mesh will be the number of rows of P, and the dimension of the simplexes will be the number of rows of T.

  • M = Mesh('load', string filename) Load a mesh from a getfem++ ascii mesh file.

    See also Mesh.save(string filename).

  • M = Mesh('from string', string s) Load a mesh from a string description.

    For example, a string returned by Mesh.char().

  • M = Mesh('import', string format, string filename) Import a mesh.

    format may be:

    • ‘gmsh’ for a mesh created with Gmsh
    • ‘gid’ for a mesh created with GiD
    • ‘am_fmt’ for a mesh created with EMC2
  • M = Mesh('clone', Mesh m2) Create a copy of a mesh.

add_convex(GT, PTS)

Add a new convex into the mesh.

The convex structure (triangle, prism,...) is given by GT (obtained with GeoTrans(‘...’)), and its points are given by the columns of PTS. On return, CVIDs contains the convex #ids. PTS might be a 3-dimensional array in order to insert more than one convex (or a two dimensional array correctly shaped according to Fortran ordering).

add_point(PTS)

Insert new points in the mesh and return their #ids.

PTS should be an nxm matrix , where n is the mesh dimension, and m is the number of points that will be added to the mesh. On output, PIDs contains the point #ids of these new points.

Remark: if some points are already part of the mesh (with a small tolerance of approximately 1e-8), they won’t be inserted again, and PIDs will contain the previously assigned #ids of these points.

boundaries()
DEPRECATED FUNCTION. Use ‘regions’ instead.
boundary()
DEPRECATED FUNCTION. Use ‘region’ instead.
char()
Output a string description of the mesh.
convex_area(CVIDs=None)
Return an estimation of the area of each convex.
curved_edges(N, CVLST=None)

[OBSOLETE FUNCTION! will be removed in a future release]

More sophisticated version of Mesh.edges() designed for curved elements. This one will return N (N>=2) points of the (curved) edges. With N==2, this is equivalent to Mesh.edges(). Since the points are no more always part of the mesh, their coordinates are returned instead of points number, in the array E which is a [ mesh_dim x 2 x nb_edges ] array. If the optional output argument C is specified, it will contain the convex number associated with each edge.

cvid()

Return the list of all convex #id.

Note that their numbering is not supposed to be contiguous from 0 to Mesh.nbcvs()-1, especially if some points have been removed from the mesh. You can use Mesh.optimize_structure() to enforce a contiguous numbering.

cvid_from_pid(PIDs, share=False)

Search convex #ids related with the point #ids given in PIDs.

If share=False, search convex whose vertex #ids are in PIDs. If share=True, search convex #ids that share the point #ids given in PIDs. CVIDs is a vector (possibly empty).

cvstruct(CVIDs=None)

Return an array of the convex structures.

If CVIDs is not given, all convexes are considered. Each convex structure is listed once in S, and CV2S maps the convexes indice in CVIDs to the indice of its structure in S.

del_convex(CVIDs)

Remove one or more convexes from the mesh.

CVIDs should contain the convexes #ids, such as the ones returned by the ‘add convex’ command.

del_convex_of_dim(DIMs)

Remove all convexes of dimension listed in DIMs.

For example; Mesh.del_convex_of_dim([1,2]) remove all line segments, triangles and quadrangles.

del_point(PIDs)

Removes one or more points from the mesh.

PIDs should contain the point #ids, such as the one returned by the ‘add point’ command.

delete_boundary(rnum, CVFIDs)
DEPRECATED FUNCTION. Use ‘delete region’ instead.
delete_region(RIDs)
Remove the regions whose #ids are listed in RIDs
dim()
Get the dimension of the mesh (2 for a 2D mesh, etc).
display()
displays a short summary for a Mesh object.
edges(CVLST=None, *args)

Synopsis: [E,C] = Mesh.edges(self [, CVLST][, ‘merge’])

[OBSOLETE FUNCTION! will be removed in a future release]

Return the list of edges of mesh M for the convexes listed in the row vector CVLST. E is a 2 x nb_edges matrix containing point indices. If CVLST is omitted, then the edges of all convexes are returned. If CVLST has two rows then the first row is supposed to contain convex numbers, and the second face numbers, of which the edges will be returned. If ‘merge’ is indicated, all common edges of convexes are merged in a single edge. If the optional output argument C is specified, it will contain the convex number associated with each edge.

export_to_dx(filename, *args)

Synopsis: Mesh.export_to_dx(self, string filename, ... [,’ascii’][,’append’][,’as’,string name,[,’serie’,string serie_name]][,’edges’])

Exports a mesh to an OpenDX file.

See also MeshFem.export_to_dx(), Slice.export_to_dx().

export_to_pos(filename, name=None)

Exports a mesh to a POS file .

See also MeshFem.export_to_pos(), Slice.export_to_pos().

export_to_vtk(filename, *args)

Synopsis: Mesh.export_to_vtk(self, string filename, ... [,’ascii’][,’quality’])

Exports a mesh to a VTK file .

If ‘quality’ is specified, an estimation of the quality of each convex will be written to the file.

See also MeshFem.export_to_vtk(), Slice.export_to_vtk().

faces_from_cvid(CVIDs=None, *args)

Synopsis: CVFIDs = Mesh.faces_from_cvid(self[, ivec CVIDs][, ‘merge’])

Return a list of convexes faces from a list of convex #id.

CVFIDs is a two-rows matrix, the first row lists convex #ids, and the second lists face numbers (local number in the convex). If CVIDs is not given, all convexes are considered. The optional argument ‘merge’ merges faces shared by the convex of CVIDs.

faces_from_pid(PIDs)

Return the convex faces whose vertex #ids are in PIDs.

CVFIDs is a two-rows matrix, the first row lists convex #ids, and the second lists face numbers (local number in the convex). For a convex face to be returned, EACH of its points have to be listed in PIDs.

geotrans(CVIDs=None)

Returns an array of the geometric transformations.

See also Mesh.cvstruct().

max_cvid()
Return the maximum #id of all convexes in the mesh (see ‘max pid’).
max_pid()
Return the maximum #id of all points in the mesh (see ‘max cvid’).
memsize()
Return the amount of memory (in bytes) used by the mesh.
merge(m2)

Merge with the Mesh m2.

Overlapping points won’t be duplicated. If m2 is a MeshFem object, its linked mesh will be used.

nbcvs()
Get the number of convexes of the mesh.
nbpts()
Get the number of points of the mesh.
normal_of_face(cv, f, nfpt=None)

Evaluates the normal of convex cv, face f at the nfpt point of the face.

If nfpt is not specified, then the normal is evaluated at each geometrical node of the face.

normal_of_faces(CVFIDs)

Evaluates (at face centers) the normals of convexes.

CVFIDs is supposed a two-rows matrix, the first row lists convex #ids, and the second lists face numbers (local number in the convex).

optimize_structure()

Reset point and convex numbering.

After optimisation, the points (resp. convexes) will be consecutively numbered from 0 to Mesh.max_pid()-1 (resp. Mesh.max_cvid()-1).

orphaned_pid()
Search point #id which are not linked to a convex.
outer_faces(CVIDs=None)

Return the faces which are not shared by two convexes.

CVFIDs is a two-rows matrix, the first row lists convex #ids, and the second lists face numbers (local number in the convex). If CVIDs is not given, all convexes are considered, and it basically returns the mesh boundary. If CVIDs is given, it returns the boundary of the convex set whose #ids are listed in CVIDs.

pid()

Return the list of points #id of the mesh.

Note that their numbering is not supposed to be contiguous from 0 to Mesh.nbpts()-1, especially if some points have been removed from the mesh. You can use Mesh.optimize_structure() to enforce a contiguous numbering.

pid_from_coords(PTS, radius=0)

Search point #id whose coordinates are listed in PTS.

PTS is an array containing a list of point coordinates. On return, PIDs is a vector containing points #id for each point found in eps range, and -1 for those which where not found in the mesh.

pid_from_cvid(CVIDs=None)

Return the points attached to each convex of the mesh.

If CVIDs is omitted, all the convexes will be considered (equivalent to CVIDs = Mesh.max_cvid()). IDx is a vector, length(IDx) = length(CVIDs)+1. Pid is a vector containing the concatenated list of #id of points of each convex in CVIDs. Each entry of IDx is the position of the corresponding convex point list in Pid. Hence, for example, the list of #id of points of the second convex is Pid[IDx(2):IDx(3)].

If CVIDs contains convex #id which do not exist in the mesh, their point list will be empty.

pid_in_cvids(CVIDs)

Search point #id listed in CVIDs.

PIDs is a vector containing points #id.

pid_in_faces(CVFIDs)

Search point #id listed in CVFIDs.

CVFIDs is a two-rows matrix, the first row lists convex #ids, and the second lists face numbers. On return, PIDs is a vector containing points #id.

pid_in_regions(RIDs)

Search point #id listed in RIDs.

PIDs is a vector containing points #id.

pts(PIDs=None)

Return the list of point coordinates of the mesh.

Each column of the returned matrix contains the coordinates of one point. If the optional argument PIDs was given, only the points whose #id is listed in this vector are returned. Otherwise, the returned matrix will have Mesh.max_pid() columns, which might be greater than Mesh.nbpts() (if some points of the mesh have been destroyed and no call to Mesh.optimize_structure() have been issued). The columns corresponding to deleted points will be filled with NaN. You can use Mesh.pid() to filter such invalid points.

pts_from_cvid(CVIDs=None)

Search point listed in CVID.

If CVIDs is omitted, all the convexes will be considered (equivalent to CVIDs = Mesh.max_cvid()). IDx is a vector, length(IDx) = length(CVIDs)+1. Pts is a vector containing the concatenated list of points of each convex in CVIDs. Each entry of IDx is the position of the corresponding convex point list in Pts. Hence, for example, the list of points of the second convex is Pts[:,IDx[2]:IDx[3]].

If CVIDs contains convex #id which do not exist in the mesh, their point list will be empty.

quality(CVIDs=None)
Return an estimation of the quality of each convex (0 <= Q <= 1).
refine(CVIDs=None)

Use a Bank strategy for mesh refinement.

If CVIDs is not given, the whole mesh is refined. Note that the regions, and the finite element methods and integration methods of the MeshFem and MeshIm objects linked to this mesh will be automagically refined.

region(RIDs)

Return the list of convexes/faces on the regions RIDs.

CVFIDs is a two-rows matrix, the first row lists convex #ids, and the second lists face numbers (local number in the convex). (and -1 when the whole convex is in the regions).

region_intersect(r1, r2)
Replace the region number r1 with its intersection with region number r2.
region_merge(r1, r2)
Merge region number r2 into region number r1.
region_substract(r1, r2)
Replace the region number r1 with its difference with region number r2.
regions()
Return the list of valid regions stored in the mesh.
save(filename)

Save the mesh object to an ascii file.

This mesh can be restored with Mesh(‘load’, filename).

set_boundary(rnum, CVFIDs)
DEPRECATED FUNCTION. Use ‘region’ instead.
set_pts(PTS)
Replace the coordinates of the mesh points with those given in PTS.
set_region(rnum, CVFIDs)

Assigns the region number rnum to the convex faces stored in each column of the matrix CVFIDs.

The first row of CVFIDs contains a convex #ids, and the second row contains a face number in the convex (or -1 for the whole convex (regions are usually used to store a list of convex faces, but you may also use them to store a list of convexes).

transform(T)

Applies the matrix T to each point of the mesh.

Note that T is not required to be a NxN matrix (with N = Mesh.dim()). Hence it is possible to transform a 2D mesh into a 3D one (and reciprocally).

translate(V)
Translates each point of the mesh from V.
triangulated_surface(Nrefine, CVLIST=None)

[DEPRECATED FUNCTION! will be removed in a future release]

Similar function to Mesh.curved_edges() : split (if necessary, i.e. if the geometric transformation if non-linear) each face into sub-triangles and return their coordinates in T (see also gf_compute(‘eval on P1 tri mesh’))

MeshFem

class MeshFem(*args)

GetFEM MeshFem object

This object represent a finite element method defined on a whole mesh.

General constructor for MeshFem objects

  • MF = MeshFem('load', string fname[, Mesh m]) Load a MeshFem from a file.

    If the mesh m is not supplied (this kind of file does not store the mesh), then it is read from the file fname and its descriptor is returned as the second output argument.

  • MF = MeshFem('from string', string s[, Mesh m]) Create a MeshFem object from its string description.

    See also MeshFem.char()

  • MF = MeshFem('clone', MeshFem mf) Create a copy of a MeshFem.

  • MF = MeshFem('sum', MeshFem mf1, MeshFem mf2[, MeshFem mf3[, ...]]) Create a MeshFem that combines two (or more) MeshFem’s.

    All MeshFem must share the same mesh (see Fem('interpolated_fem') to map a MeshFem onto another).

    After that, you should not modify the FEM of mf1, mf2 etc.

  • MF = MeshFem('levelset', MeshLevelSet mls, MeshFem mf) Create a MeshFem that is conformal to implicit surfaces defined in MeshLevelSet.

  • MF = MeshFem('global function', Mesh m, LevelSet ls, (GlobalFunction GF1,...)[, int Qdim_m]) Create a MeshFem whose base functions are global function given by the user.

  • MF = MeshFem('partial', MeshFem mf, ivec DOFs[, ivec RCVs]) Build a restricted MeshFem by keeping only a subset of the degrees of freedom of mf.

    If RCVs is given, no FEM will be put on the convexes listed in RCVs.

  • MF = MeshFem(Mesh m[, int Qdim_m=1[, int Qdim_n=1]]) Build a new MeshFem object.

    Qdim_m and Qdim_n parameters are optionals. Returns the handle of the created object.

basic_dof_from_cv(CVids)

Return the dof of the convexes listed in CVids.

WARNING: the Degree of Freedom might be returned in ANY order, do not use this function in your assembly routines. Use ‘basic dof from cvid’ instead, if you want to be able to map a convex number with its associated degrees of freedom.

One can also get the list of basic dof on a set on convex faces, by indicating on the second row of CVids the faces numbers (with respect to the convex number on the first row).

basic_dof_from_cvid(CVids=None)

Return the degrees of freedom attached to each convex of the mesh.

If CVids is omitted, all the convexes will be considered (equivalent to CVids = 1 ... Mesh.max_cvid()).

IDx is a vector, length(IDx) = length(CVids)+1. DOFs is a vector containing the concatenated list of dof of each convex in CVids. Each entry of IDx is the position of the corresponding convex point list in DOFs. Hence, for example, the list of points of the second convex is DOFs[IDx(2):IDx(3)].

If CVids contains convex #id which do not exist in the mesh, their point list will be empty.

basic_dof_nodes(DOFids=None)

Get location of basic degrees of freedom.

Return the list of interpolation points for the specified dof #IDs in DOFids (if DOFids is omitted, all basic dof are considered).

basic_dof_on_region(Rs)

Return the list of basic dof (before the optional reduction) lying on one of the mesh regions listed in Rs.

More precisely, this function returns the basic dof whose support is non-null on one of regions whose #ids are listed in Rs (note that for boundary regions, some dof nodes may not lie exactly on the boundary, for example the dof of Pk(n,0) lies on the center of the convex, but the base function in not null on the convex border).

char(opt=None)

Output a string description of the MeshFem.

By default, it does not include the description of the linked mesh object, except if opt is ‘with_mesh’.

convex_index()
Return the list of convexes who have a FEM.
display()
displays a short summary for a MeshFem object.
dof_from_cv(CVids)
Deprecated function. Use MeshFem.basic_dof_from_cv() instead.
dof_from_cvid(CVids=None)
Deprecated function. Use MeshFem.basic_dof_from_cvid() instead.
dof_from_im(mim, p=None)

Return a selection of dof who contribute significantly to the mass-matrix that would be computed with mf and the integration method mim.

p represents the dimension on what the integration method operates (default p = mesh dimension).

IMPORTANT: you still have to set a valid integration method on the convexes which are not crosses by the levelset!

dof_nodes(DOFids=None)
Deprecated function. Use MeshFem.basic_dof_nodes() instead.
dof_on_region(Rs)

Return the list of dof (after the optional reduction) lying on one of the mesh regions listed in Rs.

More precisely, this function returns the basic dof whose support is non-null on one of regions whose #ids are listed in Rs (note that for boundary regions, some dof nodes may not lie exactly on the boundary, for example the dof of Pk(n,0) lies on the center of the convex, but the base function in not null on the convex border).

For a reduced mesh_fem a dof is lying on a region if its potential corresponding shape function is nonzero on this region. The extension matrix is used to make the correspondance between basic and reduced dofs.

dof_partition()

Get the ‘dof_partition’ array.

Return the array which associates an integer (the partition number) to each convex of the MeshFem. By default, it is an all-zero array. The degrees of freedom of each convex of the MeshFem are connected only to the dof of neighbouring convexes which have the same partition number, hence it is possible to create partially discontinuous MeshFem very easily.

eval(expression, gl={}, lo={})

interpolate an expression on the (lagrangian) MeshFem.

Examples:

mf.eval('x[0]*x[1]') # interpolates the function 'x*y'
mf.eval('[x[0],x[1]]') # interpolates the vector field '[x,y]'

import numpy as np
mf.eval('np.sin(x[0])',globals(),locals()) # interpolates the function sin(x)
export_to_dx(filename, *args)

Synopsis: MeshFem.export_to_dx(self,string filename, ...[‘as’, string mesh_name][,’edges’][‘serie’,string serie_name][,’ascii’][,’append’], U, ‘name’...)

Export a MeshFem and some fields to an OpenDX file.

This function will fail if the MeshFem mixes different convex types (i.e. quads and triangles), or if OpenDX does not handle a specific element type (i.e. prism connections are not known by OpenDX).

The FEM will be mapped to order 1 Pk (or Qk) FEMs. If you need to represent high-order FEMs or high-order geometric transformations, you should consider Slice.export_to_dx().

export_to_pos(filename, name=None, *args)

Synopsis: MeshFem.export_to_pos(self,string filename[, string name][[,MeshFem mf1], mat U1, string nameU1[[,MeshFem mf2], mat U2, string nameU2,...]])

Export a MeshFem and some fields to a pos file.

The FEM and geometric transformations will be mapped to order 1 isoparametric Pk (or Qk) FEMs (as GMSH does not handle higher order elements).

export_to_vtk(filename, *args)

Synopsis: MeshFem.export_to_vtk(self,string filename, ... [‘ascii’], U, ‘name’...)

Export a MeshFem and some fields to a vtk file.

The FEM and geometric transformations will be mapped to order 1 or 2 isoparametric Pk (or Qk) FEMs (as VTK does not handle higher order elements). If you need to represent high-order FEMs or high-order geometric transformations, you should consider Slice.export_to_vtk().

extension_matrix()
Return the optional extension matrix.
fem(CVids=None)

Return a list of FEM used by the MeshFem.

FEMs is an array of all Fem objects found in the convexes given in CVids. If CV2F was supplied as an output argument, it contains, for each convex listed in CVids, the index of its correspounding FEM in FEMs.

Convexes which are not part of the mesh, or convexes which do not have any FEM have their correspounding entry in CV2F set to -1.

has_linked_mesh_levelset()
Is a mesh_fem_level_set or not.
interpolate_convex_data(Ucv)

Interpolate data given on each convex of the mesh to the MeshFem dof. The MeshFem has to be lagrangian, and should be discontinuous (typically a FEM_PK(N,0) or FEM_QK(N,0) should be used).

The last dimension of the input vector Ucv should have Mesh.max_cvid() elements.

Example of use: MeshFem.interpolate_convex_data(Mesh.quality())

is_equivalent(CVids=None)

Test if the MeshFem is equivalent.

See MeshFem.is_lagrangian()

is_lagrangian(CVids=None)

Test if the MeshFem is Lagrangian.

Lagrangian means that each base function Phi[i] is such that Phi[i](P[j]) = delta(i,j), where P[j] is the dof location of the jth base function, and delta(i,j) = 1 if i==j, else 0.<Par>

If CVids is omitted, it returns 1 if all convexes in the mesh are Lagrangian. If CVids is used, it returns the convex indices (with respect to CVids) which are Lagrangian.

is_polynomial(CVids=None)

Test if all base functions are polynomials.

See MeshFem.is_lagrangian()

is_reduced()
Return 1 if the optional reduction matrix is applied to the dofs.
linked_mesh()
Return a reference to the Mesh object linked to mf.
linked_mesh_levelset()
if it is a mesh_fem_level_set gives the linked mesh_level_set.
memsize()

Return the amount of memory (in bytes) used by the mesh_fem object.

The result does not take into account the linked mesh object.

mesh()
Return a reference to the Mesh object linked to mf. (identical to Mesh.linked_mesh())
nb_basic_dof()
Return the number of basic degrees of freedom (dof) of the MeshFem.
nbdof()
Return the number of degrees of freedom (dof) of the MeshFem.
non_conformal_basic_dof(CVids=None)

Return partially linked degrees of freedom.

Return the basic dof located on the border of a convex and which belong to only one convex, except the ones which are located on the border of the mesh. For example, if the convex ‘a’ and ‘b’ share a common face, ‘a’ has a P1 FEM, and ‘b’ has a P2 FEM, then the basic dof on the middle of the face will be returned by this function (this can be useful when searching the interfaces between classical FEM and hierarchical FEM).

non_conformal_dof(CVids=None)
Deprecated function. Use MeshFem.non_conformal_basic_dof() instead.
qdim()

Return the dimension Q of the field interpolated by the MeshFem.

By default, Q=1 (scalar field). This has an impact on the dof numbering.

reduction(s)
Set or unset the use of the reduction/extension matrices.
reduction_matrices(R, E)
Set the reduction and extension matrices and valid their use.
reduction_matrix()
Return the optional reduction matrix.
save(filename, opt=None)
Save a MeshFem in a text file (and optionaly its linked mesh object if opt is the string ‘with_mesh’).
set_classical_discontinuous_fem(K, alpha=None, *args)

Synopsis: MeshFem.set_classical_discontinuous_fem(self, int K[, @tscalar alpha[, ivec CVIDX]])

Assigns a classical (Lagrange polynomial) discontinuous fem or order K.

Similar to MeshFem.classical_fem() except that FEM_PK_DISCONTINUOUS is used. Param alpha the node inset, 0 <= alpha < 1, where 0 implies usual dof nodes, greater values move the nodes toward the center of gravity, and 1 means that all degrees of freedom collapse on the center of gravity.

set_classical_fem(k, CVids=None)

Assign a classical (Lagrange polynomial) fem of order k to the MeshFem.

Uses FEM_PK for simplexes, FEM_QK for parallelepipeds etc.

set_dof_partition(DOFP)

Change the ‘dof_partition’ array.

DOFP is a vector holding a integer value for each convex of the MeshFem. See MeshFem.dof_partition() for a description of “dof partition”.

set_fem(f, CVids=None)

Set the Finite Element Method.

Assign a FEM f to all convexes whose #ids are listed in CVids. If CVids is not given, the integration is assigned to all convexes.

See the help of Fem to obtain a list of available FEM methods.

set_partial(DOFs, RCVs=None)

Can only be applied to a partial MeshFem. Change the subset of the degrees of freedom of mf.

If RCVs is given, no FEM will be put on the convexes listed in RCVs.

set_qdim(Q)

Change the Q dimension of the field that is interpolated by the MeshFem.

Q = 1 means that the MeshFem describes a scalar field, Q = N means that the MeshFem describes a vector field of dimension N.

MeshIm

class MeshIm(*args)

GetFEM MeshIm object

This object represent an integration method defined on a whole mesh (an potentialy on its boundaries).

General constructor for MeshIm objects

  • MIM = MeshIm('load', string fname[, Mesh m]) Load a MeshIm from a file.

    If the mesh m is not supplied (this kind of file does not store the mesh), then it is read from the file and its descriptor is returned as the second output argument.

  • MIM = MeshIm('from string', string s[, Mesh m]) Create a MeshIm object from its string description.

    See also MeshIm.char()

  • MIM = MeshIm('clone', MeshIm mim) Create a copy of a MeshIm.

  • MIM = MeshIm('levelset', MeshLevelSet mls, string where, Integ im[, Integ im_tip[, Integ im_set]]) Build an integration method conformal to a partition defined implicitely by a levelset.

    The where argument define the domain of integration with respect to the levelset, it has to be chosen among ‘ALL’, ‘INSIDE’, ‘OUTSIDE’ and ‘BOUNDARY’.

  • MIM = MeshIm(Mesh m, [{Integ im|int im_degree}]) Build a new MeshIm object.

    For convenience, optional arguments (im or im_degree) can be provided, in that case a call to MeshIm.integ() is issued with these arguments.

adapt()
For a MeshIm levelset object only. Adapt the integration methods to a change of the levelset function.
char()

Output a string description of the MeshIm.

By default, it does not include the description of the linked Mesh object.

convex_index()

Return the list of convexes who have a integration method.

Convexes who have the dummy IM_NONE method are not listed.

display()
displays a short summary for a MeshIm object.
eltm(em, cv, f=None)

Return the elementary matrix (or tensor) integrated on the convex cv.

WARNING

Be sure that the fem used for the construction of em is compatible with the fem assigned to element cv ! This is not checked by the function ! If the argument f is given, then the elementary tensor is integrated on the face f of cv instead of the whole convex.

im_nodes(CVids=None)

Return the coordinates of the integration points, with their weights.

CVids may be a list of convexes, or a list of convex faces, such as returned by Mesh.region()

WARNING

Convexes which are not part of the mesh, or convexes which do not have an approximate integration method don’t have their correspounding entry (this has no meaning for exact integration methods!).

integ(CVids=None)

Return a list of integration methods used by the MeshIm.

I is an array of all Integ objects found in the convexes given in CVids. If CV2I was supplied as an output argument, it contains, for each convex listed in CVids, the index of its correspounding integration method in I.

Convexes which are not part of the mesh, or convexes which do not have any integration method have their correspounding entry in CV2I set to -1.

linked_mesh()
Returns a reference to the Mesh object linked to mim.
memsize()

Return the amount of memory (in bytes) used by the MeshIm object.

The result does not take into account the linked Mesh object.

save(filename)
Saves a MeshIm in a text file (and optionaly its linked mesh object).
set_integ(*args)

Synopsis: MeshIm.set_integ(self,{Integ im|int im_degree}[, ivec CVids])

Set the integration method.

Assign an integration method to all convexes whose #ids are listed in CVids. If CVids is not given, the integration is assigned to all convexes. It is possible to assign a specific integration method with an integration method handle im obtained via Integ(‘IM_SOMETHING’), or to let getfem choose a suitable integration method with im_degree (choosen such that polynomials of degree <= im_degree are exactly integrated. If im_degree=-1, then the dummy integration method IM_NONE will be used.)

MeshLevelSet

class MeshLevelSet(*args)

GetFEM MeshLevelSet object

General constructor for mesh_levelset objects. The role of this object is to provide a mesh cut by a certain number of level_set. This object is used to build conformal integration method (object mim and enriched finite element methods (Xfem)).

General constructor for MeshLevelSet objects

  • MLS = MeshLevelSet(Mesh m) Build a new MeshLevelSet object from a Mesh and returns its handle.
adapt()

Do all the work (cut the convexes with the levelsets).

To initialice the MeshLevelSet object or to actualize it when the value of any levelset function is modified, one has to call this method.

add(ls)

Add a link to the LevelSet ls.

Only a reference is kept, no copy is done. In order to indicate that the linked Mesh is cut by a LevelSet one has to call this method, where ls is an LevelSet object. An arbitrary number of LevelSet can be added.

WARNING

The Mesh of ls and the linked Mesh must be the same.

char()

Output a (unique) string representation of the MeshLevelSetn.

This can be used to perform comparisons between two different MeshLevelSet objects. This function is to be completed.

crack_tip_convexes()
Return the list of convex #id’s of the linked Mesh on which have a tip of any linked LevelSet’s.
cut_mesh()
Return a Mesh cut by the linked LevelSet’s.
display()
displays a short summary for a MeshLevelSet object.
levelsets()
Return a list of references to the linked LevelSet’s.
linked_mesh()
Return a reference to the linked Mesh.
memsize()
Return the amount of memory (in bytes) used by the MeshLevelSet.
nb_ls()
Return the number of linked LevelSet’s.
sup(ls)
Remove a link to the LevelSet ls.

Model

class Model(*args)

GetFEM Model object

Model variables store the variables and the state data and the description of a model. This includes the global tangent matrix, the right hand side and the constraints. There are two kinds of models, the real and the complex models.

Model object is the evolution for getfem++ 4.0 of the MdState object.

General constructor for Model objects

  • MD = Model('real') Build a model for real unknowns.
  • MD = Model('complex') Build a model for complex unknowns.
add_Dirichlet_condition_with_multipliers(mim, varname, mult_description, region, dataname=None)
Add a Dirichlet condition on the variable varname and the mesh region region. This region should be a boundary. The Dirichlet condition is prescribed with a multiplier variable described by mult_description. If mult_description is a string this is assumed to be the variable name correpsonding to the multiplier (which should be first declared as a multiplier variable on the mesh region in the model). If it is a finite element method (mesh_fem object) then a multiplier variable will be added to the model and build on this finite element method (it will be restricted to the mesh region region and eventually some conflicting dofs with some other multiplier variables will be suppressed). If it is an integer, then a multiplier variable will be added to the model and build on a classical finite element of degree that integer. dataname is the optional right hand side of the Dirichlet condition. It could be constant or described on a fem; scalar or vector valued, depending on the variable on which the Dirichlet condition is prescribed. Return the brick index in the model.
add_Dirichlet_condition_with_penalization(mim, varname, coeff, region, dataname=None)
Add a Dirichlet condition on the variable varname and the mesh region region. This region should be a boundary. The Dirichlet condition is prescribed with penalization. The penalization coefficient is intially coeff and will be added to the data of the model. dataname is the optional right hand side of the Dirichlet condition. It could be constant or described on a fem; scalar or vector valued, depending on the variable on which the Dirichlet condition is prescribed. Return the brick index in the model.
add_Fourier_Robin_brick(mim, varname, dataname, region)
Add a Fourier-Robin term to the model relatively to the variable varname. This corresponds to a weak term of the form \int (qu).v. dataname should contain the parameter q of the Fourier-Robin condition. region is the mesh region on which the term is added. Return the brick index in the model.
add_Helmholtz_brick(mim, varname, dataname, region=None)
Add a Helmholtz term to the model relatively to the variable varname. dataname should contain the wave number. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_Laplacian_brick(mim, varname, region=None)
Add a Laplacian term to the model relatively to the variable varname. If this is a vector valued variable, the Laplacian term is added componentwise. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_basic_contact_brick(varname_u, multname_n, multname_t=None, *args)

Synopsis: ind = Model.add_basic_contact_brick(self, string varname_u, string multname_n[, string multname_t], string dataname_r, Spmat BN[, Spmat BT, string dataname_friction_coeff][, string dataname_gap[, string dataname_alpha[, int symmetrized]])

Add a contact with or without friction brick to the model. If U is the vector of degrees of freedom on which the unilateral constraint is applied, the matrix BN have to be such that this constraint is defined by B_N U \le 0. A friction condition can be considered by adding the three parameters multname_t, BT and dataname_friction_coeff. In this case, the tangential displacement is B_T U and the matrix BT should have as many rows as BN multiplied by d-1 where d is the domain dimension. In this case also, dataname_friction_coeff is a data which represents the coefficient of friction. It can be a scalar or a vector representing a value on each contact condition. The unilateral constraint is prescribed thank to a multiplier multname_n whose dimension should be equal to the number of rows of BN. If a friction condition is added, it is prescribed with a multiplier multname_t whose dimension should be equal to the number of rows of BT. The augmentation parameter r should be chosen in a range of acceptabe values (see Getfem user documentation). dataname_gap is an optional parameter representing the initial gap. It can be a single value or a vector of value. dataname_alpha is an optional homogenization parameter for the augmentation parameter (see Getfem user documentation). The parameter symmetrized indicates that the symmetry of the tangent matrix will be kept or not (except for the part representing the coupling between contact and friction which cannot be symmetrized).

add_basic_d2_on_dt2_brick(mim, varnameU, datanameV, dataname_dt, dataname_alpha, dataname_rho=None, *args)

Synopsis: ind = Model.add_basic_d2_on_dt2_brick(self, MeshIm mim, string varnameU, string datanameV, string dataname_dt, string dataname_alpha,[, string dataname_rho[, int region]])

Add the standard discretization of a second order time derivative on varnameU. datanameV is a data represented on the same finite element method as U which represents the time derivative of U. The parameter dataname_rho is the density which could be omitted (the defaul value is 1). This brick should be used in addition to a time dispatcher for the other terms. The time derivative v of the variable u is preferably computed as a post-traitement which depends on each scheme. The parameter dataname_alpha depends on the time integration scheme. Return the brick index in the model.

add_basic_d_on_dt_brick(mim, varnameU, dataname_dt, dataname_rho=None, *args)

Synopsis: ind = Model.add_basic_d_on_dt_brick(self, MeshIm mim, string varnameU, string dataname_dt[, string dataname_rho[, int region]])

Add the standard discretization of a first order time derivative on varnameU. The parameter dataname_rho is the density which could be omitted (the defaul value is 1). This brick should be used in addition to a time dispatcher for the other terms. Return the brick index in the model.

add_constraint_with_multipliers(varname, multname, B, L)
Add an additional explicit constraint on the variable varname thank to a multiplier multname peviously added to the model (should be a fixed size variable). The constraint is BU=L with B being a rectangular sparse matrix. It is possible to change the constraint at any time whith the methods Model.set_private_matrix() and Model.set_private_rhs(). Return the brick index in the model.
add_constraint_with_penalization(varname, coeff, B, L)
Add an additional explicit penalized constraint on the variable varname. The constraint is :math`BU=L` with B being a rectangular sparse matrix. Be aware that B should not contain a palin row, otherwise the whole tangent matrix will be plain. It is possible to change the constraint at any time whith the methods Model.set_private_matrix() and Model.set_private_rhs(). The method Model.change_penalization_coeff() can be used. Return the brick index in the model.
add_contact_with_rigid_obstacle_brick(mim, varname_u, multname_n, multname_t=None, *args)

Synopsis: ind = Model.add_contact_with_rigid_obstacle_brick(self, MeshIm mim, string varname_u, string multname_n[, string multname_t], string dataname_r[, string dataname_friction_coeff], int region, string obstacle[, int symmetrized])

Add a contact with or without friction condition with a rigid obstacle to the model. The condition is applied on the variable varname_u on the boundary corresponding to region. The rigid obstacle should be described with the string obstacle being a signed distance to the obstacle. This string should be an expression where the coordinates are ‘x’, ‘y’ in 2D and ‘x’, ‘y’, ‘z’ in 3D. For instance, if the rigid obstacle correspond to z \le 0, the corresponding signed distance will be simply “z”. multname_n should be a fixed size variable whose size is the number of degrees of freedom on boundary region. It represent the contact equivalent nodal forces. In order to add a friction condition one has to add the multname_t and dataname_friction_coeff parameters. multname_t should be a fixed size variable whose size is the number of degrees of freedom on boundary region multiplied by d-1 where d is the domain dimension. It represent the friction equivalent nodal forces. The augmentation parameter r should be chosen in a range of acceptabe values (close to the Young modulus of the elastic body, see Getfem user documentation). dataname_friction_coeff is the friction coefficient. It could be a scalar or a vector of values representing the friction coefficient on each contact node. The parameter symmetrized indicates that the symmetry of the tangent matrix will be kept or not. Basically, this brick compute the matrix BN and the vectors gap and alpha and calls the basic contact brick.

add_data(name, size, niter=None)
Add a data to the model of constant size. name is the data name and niter is the optional number of version of the data stored, for time integration schemes.
add_explicit_matrix(varname1, varname2, B, issymmetric=None, *args)

Synopsis: ind = Model.add_explicit_matrix(self, string varname1, string varname2, Spmat B[, int issymmetric[, int iscoercive]])

Add a brick representing an explicit matrix to be added to the tangent linear system relatively to the variables ‘varname1’ and ‘varname2’. The given matrix should have has many rows as the dimension of ‘varname1’ and as many columns as the dimension of ‘varname2’. If the two variables are different and if issymmetric’ is set to 1 then the transpose of the matrix is also added to the tangent system (default is 0). Set `iscoercive to 1 if the term does not affect the coercivity of the tangent system (default is 0). The matrix can be changed by the command Model.set_private_matrix(). Return the brick index in the model.

add_explicit_rhs(varname, L)
Add a brick representing an explicit right hand side to be added to the right hand side of the tangent linear system relatively to the variable ‘varname’. The given rhs should have the same size than the dimension of ‘varname’. The rhs can be changed by the command Model.set_private_rhs(). Return the brick index in the model.
add_fem_data(name, mf, qdim=None, *args)

Synopsis: Model.add_fem_data(self, string name, MeshFem mf[, int qdim[, int niter]])

Add a data to the model linked to a MeshFem. name is the data name, qdim is the optional dimension of the data over the MeshFem and niter is the optional number of version of the data stored, for time integration schemes.

add_fem_variable(name, mf, niter=None)
Add a variable to the model linked to a MeshFem. name is the variable name and niter is the optional number of version of the data stored, for time integration schemes.
add_generalized_Dirichlet_condition_with_multipliers(mim, varname, mult_description, region, dataname, Hname)
Add a Dirichlet condition on the variable varname and the mesh region region. This version is for vector field. It prescribes a condition Hu = r where H is a matrix field. The region should be a boundary. The Dirichlet condition is prescribed with a multiplier variable described by mult_description. If mult_description is a string this is assumed to be the variable name corresponding to the multiplier (which should be first declared as a multiplier variable on the mesh region in the model). If it is a finite element method (mesh_fem object) then a multiplier variable will be added to the model and build on this finite element method (it will be restricted to the mesh region region and eventually some conflicting dofs with some other multiplier variables will be suppressed). If it is an integer, then a multiplier variable will be added to the model and build on a classical finite element of degree that integer. dataname is the right hand side of the Dirichlet condition. It could be constant or described on a fem; scalar or vector valued, depending on the variable on which the Dirichlet condition is prescribed. Hname’ is the data corresponding to the matrix field `H. Return the brick index in the model.
add_generalized_Dirichlet_condition_with_penalization(mim, varname, coeff, region, dataname, Hname)
Add a Dirichlet condition on the variable varname and the mesh region region. This version is for vector field. It prescribes a condition Hu = r where H is a matrix field. The region should be a boundary. The Dirichlet condition is prescribed with penalization. The penalization coefficient is intially coeff and will be added to the data of the model. dataname is the right hand side of the Dirichlet condition. It could be constant or described on a fem; scalar or vector valued, depending on the variable on which the Dirichlet condition is prescribed. Hname’ is the data corresponding to the matrix field `H. It has to be a constant matrix or described on a scalar fem. Return the brick index in the model.
add_generic_elliptic_brick(mim, varname, dataname, region=None)
Add a generic elliptic term to the model relatively to the variable varname. The shape of the elliptic term depends both on the variable and the data. This corresponds to a term -\text{div}(a\nabla u) where a is the data and u the variable. The data can be a scalar, a matrix or an order four tensor. The variable can be vector valued or not. If the data is a scalar or a matrix and the variable is vector valued then the term is added componentwise. An order four tensor data is allowed for vector valued variable only. The data can be constant or describbed on a fem. Of course, when the data is a tensor describe on a finite element method (a tensor field) the data can be a huge vector. The components of the matrix/tensor have to be stored with the fortran order (columnwise) in the data vector (compatibility with blas). The symmetry of the given matrix/tensor is not verified (but assumed). If this is a vector valued variable, the Laplacian term is added componentwise. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_initialized_data(name, V)
Add a fixed size data to the model linked to a MeshFem. name is the data name and V is the value of the data.
add_initialized_fem_data(name, mf, V)
Add a data to the model linked to a MeshFem. name is the data name. The data is initiakized with V. The data can be a scalar or vector field.
add_isotropic_linearized_elasticity_brick(mim, varname, dataname_lambda, dataname_mu, region=None)
Add an isotropic linearized elasticity term to the model relatively to the variable varname. dataname_lambda and dataname_mu should contain the Lam’e coefficients. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_linear_incompressibility_brick(mim, varname, multname_pressure, region=None, *args)

Synopsis: ind = Model.add_linear_incompressibility_brick(self, MeshIm mim, string varname, string multname_pressure[, int region[, string dataname_coeff]])

Add an linear incompressibility condition on variable. multname_pressure is a variable which represent the pressure. Be aware that an inf-sup condition between the finite element method describing the pressure and the primal variable has to be satisfied. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. dataname_coeff is an optional penalization coefficient for nearly incompressible elasticity for instance. In this case, it is the inverse of the Lam’e coefficient \lambda. Return the brick index in the model.

add_mass_brick(mim, varname, dataname_rho=None, *args)

Synopsis: ind = Model.add_mass_brick(self, MeshIm mim, string varname[, string dataname_rho[, int region]])

Add mass term to the model relatively to the variable varname. If specified, the data dataname_rho should contain the density (1 if omitted). region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.

add_midpoint_dispatcher(bricks_indices)
Add a midpoint time dispatcher to a list of bricks. For instance, a nonlinear term K(U) will be replaced by K((U^{n+1} +  U^{n})/2).
add_multiplier(name, mf, primalname, niter=None)
Add a particular variable linked to a fem being a multiplier with respect to a primal variable. The dof will be filtered with the gmm::range_basis function applied on the terms of the model which link the multiplier and the primal variable. This in order to retain only linearly independant constraints on the primal variable. Optimized for boundary multipliers. niter is the optional number of version of the data stored, for time integration schemes.
add_nonlinear_elasticity_brick(mim, varname, constitutive_law, dataname, region=None)
Add a nonlinear elasticity term to the model relatively to the variable varname. lawname is the constitutive law which could be ‘SaintVenant Kirchhoff’, ‘Mooney Rivlin’ or ‘Ciarlet Geymonat’. dataname is a vector of parameters for the constitutive law. Its length depends on the law. It could be a short vector of constant values or a vector field described on a finite element method for variable coefficients. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_nonlinear_incompressibility_brick(mim, varname, multname_pressure, region=None)
Add an nonlinear incompressibility condition on variable (for large strain elasticity). multname_pressure is a variable which represent the pressure. Be aware that an inf-sup condition between the finite element method describing the pressure and the primal variable has to be satisfied. region is an optional mesh region on which the term is added. If it is not specified, it is added on the whole mesh. Return the brick index in the model.
add_normal_source_term_brick(mim, varname, dataname, region)
Add a source term on the variable varname on a boundary region. This region should be a boundary. The source term is represented by the data dataname which could be constant or described on a fem. A scalar product with the outward normal unit vector to the boundary is performed. The main aim of this brick is to represent a Neumann condition with a vector data without performing the scalar product with the normal as a pre-processing. Return the brick index in the model.
add_source_term_brick(mim, varname, dataname, region=None, *args)

Synopsis: ind = Model.add_source_term_brick(self, MeshIm mim, string varname, string dataname[, int region[, string directdataname]])

Add a source term to the model relatively to the variable varname. The source term is represented by the data dataname which could be constant or described on a fem. region is an optional mesh region on which the term is added. An additional optional data directdataname can be provided. The corresponding data vector will be directly added to the right hand side without assembly. Return the brick index in the model.

add_theta_method_dispatcher(bricks_indices, theta)
Add a theta-method time dispatcher to a list of bricks. For instance, a matrix term K will be replaced by \theta K U^{n+1} + (1-\theta) K U^{n}.
add_unilateral_contact_brick(mim1, mim2=None, *args)

Synopsis: ind = Model.add_unilateral_contact_brick(self, MeshIm mim1[, MeshIm mim2], string varname_u1[, string varname_u2], string multname_n[, string multname_t], string dataname_r[, string dataname_fr], int rg1, int rg2[, int slave1, int slave2, int symmetrized])

Add a contact with or without friction condition between two faces of one or two elastic bodies. The condition is applied on the variable varname_u1 or the variables varname_u1 and varname_u2 depending if a single or two distinct displacement fields are given. Integers rg1 and rg2 represent the regions expected to come in contact with each other. In the single displacement variable case the regions defined in both rg1 and rg2 refer to the variable varname_u1. In the case of two displacement variables, rg1 refers to varname_u1 and rg2 refers to varname_u2. multname_n should be a fixed size variable whose size is the number of degrees of freedom on those regions among the ones defined in rg1 and rg2 which are characterized as “slaves”. It represents the contact equivalent nodal normal forces. multname_t should be a fixed size variable whose size corresponds to the size of multname_n multiplied by qdim - 1 . It represents the contact equivalent nodal tangent (frictional) forces. The augmentation parameter r should be chosen in a range of acceptabe values (close to the Young modulus of the elastic body, see Getfem user documentation). The friction coefficient stored in the parameter fr is either a single value or a vector of the same size as multname_n. The optional parameters slave1 and slave2 declare if the regions defined in rg1 and rg2 are correspondingly considered as “slaves”. By default slave1 is true and slave2 is false, i.e. rg1 contains the slave surfaces, while ‘rg2’ the master surfaces. Preferrably only one of slave1 and slave2 is set to true. The parameter symmetrized indicates that the symmetry of the tangent matrix will be kept or not. Basically, this brick computes the matrices BN and BT and the vectors gap and alpha and calls the basic contact brick.

add_variable(name, size, niter=None)
Add a variable to the model of constant size. name is the variable name and niter is the optional number of version of the data stored, for time integration schemes.
assembly(option=None)
Assembly of the tangent system taking into account the terms from all bricks. option, if specified, should be ‘build_all’, ‘build_rhs’ or ‘build_matrix’. The default is to build the whole tangent linear system (matrix and rhs). This function is usefull to solve your problem with you own solver.
change_penalization_coeff(ind_brick, coeff)
Change the penalization coefficient of a Dirichlet condition with penalization brick. If the brick is not of this kind, this function has an undefined behavior.
char()

Output a (unique) string representation of the Model.

This can be used to perform comparisons between two different Model objects. This function is to be completed.

clear()
Clear the model.
compute_Von_Mises_or_Tresca(varname, lawname, dataname, mf_vm, version=None)
Compute on mf_vm the Von-Mises stress or the Tresca stress of a field for nonlinear elasticity in 3D. lawname is the constitutive law which could be ‘SaintVenant Kirchhoff’, ‘Mooney Rivlin’ or ‘Ciarlet Geymonat’. dataname is a vector of parameters for the constitutive law. Its length depends on the law. It could be a short vector of constant values or a vector field described on a finite element method for variable coefficients. version should be ‘Von_Mises’ or ‘Tresca’ (‘Von_Mises’ is the default).
compute_isotropic_linearized_Von_Mises_or_Tresca(varname, dataname_lambda, dataname_mu, mf_vm, version=None)
Compute the Von-Mises stress or the Tresca stress of a field (only valid for isotropic linearized elasticity in 3D). version should be ‘Von_Mises’ or ‘Tresca’ (‘Von_Mises’ is the default).
contact_brick_set_BN(indbrick, BN)
Can be used to set the BN matrix of a basic contact/friction brick.
contact_brick_set_BT(indbrick, BT)
Can be used to set the BT matrix of a basic contact with friction brick.
disable_bricks(bricks_indices)
Disable a brick (the brick will no longer participate to the building of the tangent linear system).
display()
displays a short summary for a Model object.
first_iter()
To be executed before the first iteration of a time integration scheme.
from_variables()
Return the vector of all the degrees of freedom of the model consisting of the concatenation of the variables of the model (usefull to solve your problem with you own solver).
interval_of_variable(varname)
Gives the interval of the variable varname in the linear system of the model.
is_complex()
Return 0 is the model is real, 1 if it is complex.
listbricks()
print to the output the list of bricks of the model.
listvar()
print to the output the list of variables and constants of the model.
matrix_term(ind_brick, ind_term)
Gives the matrix term ind_term of the brick ind_brick if it exists
memsize()
Return a rough approximation of the amount of memory (in bytes) used by the model.
mult_varname_Dirichlet(ind_brick)
Gives the name of the multiplier variable for a Dirichlet brick. If the brick is not a Dirichlet condition with multiplier brick, this function has an undefined behavior
next_iter()
To be executed at the end of each iteration of a time integration scheme.
resize_variable(name, size)
Resize a constant size variable of the model. name is the variable name.
rhs()
Return the right hand side of the tangent problem.
set_private_matrix(indbrick, B)
For some specific bricks having an internal sparse matrix (explicit bricks: ‘constraint brick’ and ‘explicit matrix brick’), set this matrix.
set_private_rhs(indbrick, B)
For some specific bricks having an internal right hand side vector (explicit bricks: ‘constraint brick’ and ‘explicit rhs brick’), set this rhs.
set_variable(name, V, niter=None)
Set the value of a variable or data. name is the data name and niter is the optional number of version of the data stored, for time integration schemes.
solve(*args)

Synopsis: Model.solve(self[, ...])

Run the standard getfem solver.

Note that you should be able to use your own solver if you want (it is possible to obtain the tangent matrix and its right hand side with the Model.tangent_matrix() etc.).

Various options can be specified:

  • ‘noisy’ or ‘very_noisy’

    the solver will display some information showing the progress (residual values etc.).

  • ‘max_iter’, int NIT

    set the maximum iterations numbers.

  • ‘max_res’, @float RES

    set the target residual value.

  • ‘lsolver’, string SOLVER_NAME

    select explicitely the solver used for the linear systems (the default value is ‘auto’, which lets getfem choose itself). Possible values are ‘superlu’, ‘mumps’ (if supported), ‘cg/ildlt’, ‘gmres/ilu’ and ‘gmres/ilut’.

tangent_matrix()
Return the tangent matrix stored in the model .
to_variables(V)
Set the value of the variables of the model with the vector V. Typically, the vector V results of the solve of the tangent linear system (usefull to solve your problem with you own solver).
unable_bricks(bricks_indices)
Unable a disabled brick.
variable(name, niter=None)
Gives the value of a variable or data.
velocity_update_for_Newmark_scheme(id2dt2_brick, varnameU, datanameV, dataname_dt, dataname_twobeta, dataname_alpha)
Function which udpate the velocity v^{n+1} after the computation of the displacement u^{n+1} and before the next iteration. Specific for Newmark scheme and when the velocity is included in the data of the model.* This version inverts the mass matrix by a conjugate gradient.
velocity_update_for_order_two_theta_method(varnameU, datanameV, dataname_dt, dataname_theta)
Function which udpate the velocity v^{n+1} after the computation of the displacement u^{n+1} and before the next iteration. Specific for theta-method and when the velocity is included in the data of the model.

Precond

class Precond(*args)

GetFEM Precond object

The preconditioners may store REAL or COMPLEX values. They accept getfem sparse matrices and Matlab sparse matrices.

General constructor for Precond objects

  • PC = Precond('identity') Create a REAL identity precondioner.
  • PC = Precond('cidentity') Create a COMPLEX identity precondioner.
  • PC = Precond('diagonal', vec D) Create a diagonal precondioner.
  • PC = Precond('ildlt', SpMat m) Create an ILDLT (Cholesky) preconditioner for the (symmetric) sparse matrix m. This preconditioner has the same sparsity pattern than m (no fill-in).
  • PC = Precond('ilu', SpMat m) Create an ILU (Incomplete LU) preconditioner for the sparse matrix m. This preconditioner has the same sparsity pattern than m (no fill-in).
  • PC = Precond('ildltt', SpMat m[, int fillin[, scalar threshold]]) Create an ILDLTT (Cholesky with filling) preconditioner for the (symmetric) sparse matrix m. The preconditioner may add at most fillin additional non-zero entries on each line. The default value for fillin is 10, and the default threshold is1e-7.
  • PC = Precond('ilut', SpMat m[, int fillin[, scalar threshold]]) Create an ILUT (Incomplete LU with filling) preconditioner for the sparse matrix m. The preconditioner may add at most fillin additional non-zero entries on each line. The default value for fillin is 10, and the default threshold is 1e-7.
  • PC = Precond('superlu', SpMat m) Uses SuperLU to build an exact factorization of the sparse matrix m. This preconditioner is only available if the getfem-interface was built with SuperLU support. Note that LU factorization is likely to eat all your memory for 3D problems.
  • PC = Precond('spmat', SpMat m) Preconditionner given explicitely by a sparse matrix.
char()

Output a (unique) string representation of the Precond.

This can be used to perform comparisons between two different Precond objects. This function is to be completed.

display()
displays a short summary for a Precond object.
is_complex()
Return 1 if the preconditioner stores complex values.
mult(V)
Apply the preconditioner to the supplied vector.
size()
Return the dimensions of the preconditioner.
tmult(V)
Apply the transposed preconditioner to the supplied vector.
type()
Return a string describing the type of the preconditioner (‘ilu’, ‘ildlt’,..).

Slice

class Slice(*args)

GetFEM Slice object

Creation of a mesh slice. Mesh slices are very similar to a P1-discontinuous MeshFem on which interpolation is very fast. The slice is built from a mesh object, and a description of the slicing operation, for example:

sl = Slice(('planar',+1,[[0],[0]],[[0],[1]]), m, 5)

cuts the original mesh with the half space {y>0}. Each convex of the original Mesh m is simplexified (for example a quadrangle is splitted into 2 triangles), and each simplex is refined 5 times.

Slicing operations can be:

  • cutting with a plane, a sphere or a cylinder
  • intersection or union of slices
  • isovalues surfaces/volumes
  • “points”, “streamlines” (see below)

If the first argument is a MeshFem mf instead of a Mesh, and if it is followed by a mf-field u, then the deformation u will be applied to the mesh before the slicing operation.

The first argument can also be a slice.

General constructor for Slice objects

  • sl = Slice(sliceop, {Slice sl|{Mesh m| MeshFem mf, vec U}, int refine}[, mat CVfids]) Create a Slice using sliceop operation.

    sliceop operation is specified with Tuple or List, do not forget the extra parentheses!. The first element is the name of the operation, followed the slicing options:

    • (‘none’) : Does not cut the mesh.

    • (‘planar’, int orient, vec p, vec n) : Planar cut. p and n define a half-space, p being a point belong to the boundary of the half-space, and n being its normal. If orient is equal to -1 (resp. 0, +1), then the slicing operation will cut the mesh with the “interior” (resp. “boundary”, “exterior”) of the half-space. orient may also be set to +2 which means that the mesh will be sliced, but both the outer and inner parts will be kept.

    • (‘ball’, int orient, vec c, scalar r) : Cut with a ball of center c and radius r.

    • (‘cylinder’, int orient, vec p1, vec p2, scalar r) : Cut with a cylinder whose axis is the line (p1, p2) and whose radius is r.

    • (‘isovalues’, int orient, MeshFem mf, vec U, scalar s) : Cut using the isosurface of the field U (defined on the MeshFem mf). The result is the set {x such that `U`(x) <= `s}` or {x such that `U`(x)=`s}` or {x such that `U`(x) >= `s}` depending on the value of orient.

    • (‘boundary’[, SLICEOP]) : Return the boundary of the result of SLICEOP, where SLICEOP is any slicing operation. If SLICEOP is not specified, then the whole mesh is considered (i.e. it is equivalent to (‘boundary’,{‘none’})).

    • (‘explode’, mat Coef) : Build an ‘exploded’ view of the mesh: each convex is shrinked (0 < Coef <= 1). In the case of 3D convexes, only their faces are kept.

    • (‘union’, SLICEOP1, SLICEOP2) : Returns the union of slicing operations.

    • (‘intersection’, SLICEOP1, SLICEOP2) : Returns the intersection of slicing operations, for example:

      sl = Slice((intersection',('planar',+1,[[0],[0],[0]],[[0],[0],[1]]),
                                 ('isovalues',-1,mf2,u2,0)),mf,u,5)
    • (‘comp’, SLICEOP) : Returns the complementary of slicing operations.

    • (‘diff’, SLICEOP1, SLICEOP2) : Returns the difference of slicing operations.

    • (‘mesh’, Mesh m) : Build a slice which is the intersection of the sliced mesh with another mesh. The slice is such that all of its simplexes are stricly contained into a convex of each mesh.

  • sl = Slice('streamlines', MeshFem mf, mat U, mat S) Compute streamlines of the (vector) field U, with seed points given by the columns of S.

  • sl = Slice('points', Mesh m, mat Pts) Return the “slice” composed of points given by the columns of Pts (useful for interpolation on a given set of sparse points, see gf_compute('interpolate on',sl).

  • sl = Slice('load', string filename[, Mesh m]) Load the slice (and its linked mesh if it is not given as an argument) from a text file.

area()
Return the area of the slice.
char()

Output a (unique) string representation of the Slice.

This can be used to perform comparisons between two different Slice objects. This function is to be completed.

cvs()
Return the list of convexes of the original mesh contained in the slice.
dim()
Return the dimension of the slice (2 for a 2D mesh, etc..).
display()
displays a short summary for a Slice object.
edges()

Return the edges of the linked mesh contained in the slice.

P contains the list of all edge vertices, E1 contains the indices of each mesh edge in P, and E2 contains the indices of each “edges” which is on the border of the slice. This function is useless except for post-processing purposes.

export_to_dx(filename, *args)

Synopsis: Slice.export_to_dx(self, string filename, ...)

Export a slice to OpenDX.

Following the filename, you may use any of the following options:

  • if ‘ascii’ is not used, the file will contain binary data (non portable, but fast).
  • if ‘edges’ is used, the edges of the original mesh will be written instead of the slice content.
  • if ‘append’ is used, the opendx file will not be overwritten, and the new data will be added at the end of the file.

More than one dataset may be written, just list them. Each dataset consists of either:

  • a field interpolated on the slice (scalar, vector or tensor), followed by an optional name.
  • a mesh_fem and a field, followed by an optional name.
export_to_pos(filename, name=None, *args)

Synopsis: Slice.export_to_pos(self, string filename[, string name][[,MeshFem mf1], mat U1, string nameU1[[,MeshFem mf1], mat U2, string nameU2,...])

Export a slice to Gmsh.

More than one dataset may be written, just list them. Each dataset consists of either:

  • a field interpolated on the slice (scalar, vector or tensor).
  • a mesh_fem and a field.
export_to_pov(filename)
Export a the triangles of the slice to POV-RAY.
export_to_vtk(filename, *args)

Synopsis: Slice.export_to_vtk(self, string filename, ...)

Export a slice to VTK.

Following the filename, you may use any of the following options:

  • if ‘ascii’ is not used, the file will contain binary data (non portable, but fast).
  • if ‘edges’ is used, the edges of the original mesh will be written instead of the slice content.

More than one dataset may be written, just list them. Each dataset consists of either:

  • a field interpolated on the slice (scalar, vector or tensor), followed by an optional name.
  • a mesh_fem and a field, followed by an optional name.

Examples:

  • Slice.export_to_vtk(‘test.vtk’, Usl, ‘first_dataset’, mf, U2, ‘second_dataset’)
  • Slice.export_to_vtk(‘test.vtk’, ‘ascii’, mf,U2)
  • Slice.export_to_vtk(‘test.vtk’, ‘edges’, ‘ascii’, Uslice)
interpolate_convex_data(Ucv)

Interpolate data given on each convex of the mesh to the slice nodes.

The input array Ucv may have any number of dimensions, but its last dimension should be equal to Mesh.max_cvid().

Example of use: Slice.interpolate_convex_data(Mesh.quality()).

linked_mesh()
Return the mesh on which the slice was taken.
memsize()
Return the amount of memory (in bytes) used by the slice object.
mesh()
Return the mesh on which the slice was taken (identical to ‘linked mesh’)
nbpts()
Return the number of points in the slice.
nbsplxs(dim=None)

Return the number of simplexes in the slice.

Since the slice may contain points (simplexes of dim 0), segments (simplexes of dimension 1), triangles etc., the result is a vector of size Slice.dim()+1, except if the optional argument dim is used.

pts()
Return the list of point coordinates.
set_pts(P)

Replace the points of the slice.

The new points P are stored in the columns the matrix. Note that you can use the function to apply a deformation to a slice, or to change the dimension of the slice (the number of rows of P is not required to be equal to Slice.dim()).

splxs(dim)

Return the list of simplexes of dimension dim.

On output, S has ‘dim+1’ rows, each column contains the point numbers of a simplex. The vector CV2S can be used to find the list of simplexes for any convex stored in the slice. For example ‘S[:,CV2S[4]:CV2S[5]]’ gives the list of simplexes for the fourth convex.

Spmat

class Spmat(*args)

GetFEM Spmat object

Create a new sparse matrix in getfem++ format. These sparse matrix can be stored as CSC (compressed column sparse), which is the format used by Matlab, or they can be stored as WSC (internal format to getfem). The CSC matrices are not writable (it would be very inefficient), but they are optimized for multiplication with vectors, and memory usage. The WSC are writable, they are very fast with respect to random read/write operation. However their memory overhead is higher than CSC matrices, and they are a little bit slower for matrix-vector multiplications.

By default, all newly created matrices are build as WSC matrices. This can be changed later with Spmat.to_csc(...), or may be changed automatically by getfem (for example gf_linsolve() converts the matrices to CSC).

The matrices may store REAL or COMPLEX values.

General constructor for Spmat objects

  • SM = Spmat('empty', int m [, int n]) Create a new empty (i.e. full of zeros) sparse matrix, of dimensions m x n. If n is omitted, the matrix dimension is m x m.

  • SM = Spmat('copy', mat K [, list I [, list J]]) Duplicate a matrix K (which might be a SpMat). If index I and/or J are given, the matrix will be a submatrix of K. For example:

    m = Spmat('copy', Spmat('empty',50,50), range(40), [6, 7, 8, 3, 10])
    

    will return a 40x5 matrix.

  • SM = Spmat('identity', int n) Create a n x n identity matrix.

  • SM = Spmat('mult', Spmat A, Spmat B) Create a sparse matrix as the product of the sparse matrices A and B. It requires that A and B be both real or both complex, you may have to use Spmat.to_complex()

  • SM = Spmat('add', Spmat A, Spmat B) Create a sparse matrix as the sum of the sparse matrices A and B. Adding a real matrix with a complex matrix is possible.

  • SM = Spmat('diag', mat D [, ivec E [, int n [,int m]]]) Create a diagonal matrix. If E is given, D might be a matrix and each column of E will contain the sub-diagonal number that will be filled with the corresponding column of D.

  • SM = Spmat('load','hb'|'harwell-boeing'|'mm'|'matrix-market', string filename) Read a sparse matrix from an Harwell-Boeing or a Matrix-Market file .

add(I, J, V)

Add V to the sub-matrix ‘M(I,J)’.

V might be a sparse matrix or a full matrix.

assign(I, J, V)

Copy V into the sub-matrix ‘M(I,J)’.

V might be a sparse matrix or a full matrix.

char()

Output a (unique) string representation of the Spmat.

This can be used to perform comparisons between two different Spmat objects. This function is to be completed.

clear(I=None, *args)

Synopsis: Spmat.clear(self[, list I[, list J]])

Erase the non-zero entries of the matrix.

The optional arguments I and J may be specified to clear a sub-matrix instead of the entire matrix.

conjugate()
Conjugate each element of the matrix.
csc_ind()

Return the two usual index arrays of CSC storage.

If M is not stored as a CSC matrix, it is converted into CSC.

csc_val()

Return the array of values of all non-zero entries of M.

If M is not stored as a CSC matrix, it is converted into CSC.

diag(E=None)

Return the diagonal of M as a vector.

If E is used, return the sub-diagonals whose ranks are given in E.

dirichlet_nullspace(R)

Solve the dirichlet conditions M.U=R.

A solution U0 which has a minimum L2-norm is returned, with a sparse matrix N containing an orthogonal basis of the kernel of the (assembled) constraints matrix M (hence, the PDE linear system should be solved on this subspace): the initial problem

K.U = B with constraints M.U = R

is replaced by

(N’.K.N).UU = N’.B with U = N.UU + U0

display()
displays a short summary for a Spmat object.
full(I=None, *args)

Synopsis: Sm = Spmat.full(self[, list I[, list J]])

Return a full (sub-)matrix.

The optional arguments I and J, are the sub-intervals for the rows and columns that are to be extracted.

is_complex()
Return 1 if the matrix contains complex values.
mult(V)

Product of the sparse matrix M with a vector V.

For matrix-matrix multiplications, see Spmat(‘mult’).

nnz()
Return the number of non-null values stored in the sparse matrix.
save(format, filename)

Export the sparse matrix.

the format of the file may be ‘hb’ for Harwell-Boeing, or ‘mm’ for Matrix-Market.

scale(v)
Multiplies the matrix by a scalar value v.
set_diag(D, E=None)

Change the diagonal (or sub-diagonals) of the matrix.

If E is given, D might be a matrix and each column of E will contain the sub-diagonal number that will be filled with the corresponding column of D.

size()
Return a vector where ni and nj are the dimensions of the matrix.
storage()

Return the storage type currently used for the matrix.

The storage is returned as a string, either ‘CSC’ or ‘WSC’.

tmult(V)
Product of M transposed (conjugated if M is complex) with the vector V.
to_complex()
Store complex numbers.
to_csc()

Convert the matrix to CSC storage.

CSC storage is recommended for matrix-vector multiplications.

to_wsc()

Convert the matrix to WSC storage.

Read and write operation are quite fast with WSC storage.

transconj()
Transpose and conjugate the matrix.
transpose()
Transpose the matrix.

Module asm

General assembly function.

Many of the functions below use more than one mesh_fem: the main mesh_fem (mf_u) used for the main unknow, and data mesh_fem (mf_d) used for the data. It is always assumed that the Qdim of mf_d is equal to 1: if mf_d is used to describe vector or tensor data, you just have to “stack” (in fortran ordering) as many scalar fields as necessary.
asm_mass_matrix(mim, mf1, mf2=None)

Assembly of a mass matrix.

Return a SpMat object.

asm_laplacian(mim, mf_u, mf_d, a)

Assembly of the matrix for the Laplacian problem.

\nabla\cdot(a(x)\nabla u) with a a scalar.

Return a SpMat object.

asm_linear_elasticity(mim, mf_u, mf_d, lambda_d, mu_d)

Assembles of the matrix for the linear (isotropic) elasticity problem.

\nabla\cdot(C(x):\nabla u) with C defined via lambda_d and mu_d.

Return a SpMat object.

asm_nonlinear_elasticity(mim, mf_u, U, law, mf_d, params, *args)

Synopsis: TRHS = asm_nonlinear_elasticity(MeshIm mim, MeshFem mf_u, vec U, string law, MeshFem mf_d, mat params, {‘tangent matrix’|’rhs’|’incompressible tangent matrix’, MeshFem mf_p, vec P|’incompressible rhs’, MeshFem mf_p, vec P})

Assembles terms (tangent matrix and right hand side) for nonlinear elasticity.

The solution U is required at the current time-step. The law may be choosen among:

  • ‘SaintVenant Kirchhoff’: Linearized law, should be avoided). This law has the two usual Lame coefficients as parameters, called lambda and mu.
  • ‘Mooney Rivlin’: Only for incompressibility. This law has two parameters, called C1 and C2.
  • ‘Ciarlet Geymonat’: This law has 3 parameters, called lambda, mu and gamma, with gamma chosen such that gamma is in ]-lambda/2-mu, -mu[.

The parameters of the material law are described on the MeshFem mf_d. The matrix params should have nbdof(mf_d) columns, each row correspounds to a parameter.

The last argument selects what is to be built: either the tangent matrix, or the right hand side. If the incompressibility is considered, it should be followed by a MeshFem mf_p, for the pression.

Return a SpMat object (tangent matrix), vec object (right hand side), tuple of SpMat objects (incompressible tangent matrix), or tuple of vec objects (incompressible right hand side).

asm_stokes(mim, mf_u, mf_p, mf_d, nu)

Assembly of matrices for the Stokes problem.

-\nu(x)\Delta u + \nabla p = 0 \nabla\cdot u  = 0 with \nu (nu), the fluid’s dynamic viscosity.

On output, K is the usual linear elasticity stiffness matrix with \lambda = 0 and 2\mu = \nu. B is a matrix corresponding to \int p\nabla\cdot\phi.

K and B are SpMat object’s.

asm_helmholtz(mim, mf_u, mf_d, k)

Assembly of the matrix for the Helmholtz problem.

\Delta u + k^2 u = 0, with k complex scalar.

Return a SpMat object.

asm_bilaplacian(mim, mf_u, mf_d, a)

Assembly of the matrix for the Bilaplacian problem.

\Delta(a(x)\Delta u) = 0 with a scalar.

Return a SpMat object.

asm_volumic_source(mim, mf_u, mf_d, fd)

Assembly of a volumic source term.

Output a vector V, assembled on the MeshFem mf_u, using the data vector fd defined on the data MeshFem mf_d. fd may be real or complex-valued.

Return a vec object.

asm_boundary_source(bnum, mim, mf_u, mf_d, G)

Assembly of a boundary source term.

G should be a [Qdim x N] matrix, where N is the number of dof of mf_d, and Qdim is the dimension of the unkown u (that is set when creating the MeshFem).

Return a vec object.

asm_dirichlet(bnum, mim, mf_u, mf_d, H, R, threshold=None)

Assembly of Dirichlet conditions of type h.u = r.

Handle h.u = r where h is a square matrix (of any rank) whose size is equal to the dimension of the unkown u. This matrix is stored in H, one column per dof in mf_d, each column containing the values of the matrix h stored in fortran order:

`H(:,j) = [h11(x_j) h21(x_j) h12(x_j) h22(x_j)]`

if u is a 2D vector field.

Of course, if the unknown is a scalar field, you just have to set H = ones(1, N), where N is the number of dof of mf_d.

This is basically the same than calling gf_asm(‘boundary qu term’) for H and calling gf_asm(‘neumann’) for R, except that this function tries to produce a ‘better’ (more diagonal) constraints matrix (when possible).

See also Spmat.Dirichlet_nullspace().

asm_boundary_qu_term(boundary_num, mim, mf_u, mf_d, q)

Assembly of a boundary qu term.

q should be be a [Qdim x Qdim x N] array, where N is the number of dof of mf_d, and Qdim is the dimension of the unkown u (that is set when creating the MeshFem).

Return a SpMat object.

asm_volumic(CVLST=None, *args)

Synopsis: (...) = asm_volumic(,CVLST], expr [, mesh_ims, mesh_fems, data...])

Generic assembly procedure for volumic assembly.

The expression expr is evaluated over the MeshFem’s listed in the arguments (with optional data) and assigned to the output arguments. For details about the syntax of assembly expressions, please refer to the getfem user manual (or look at the file getfem_assembling.h in the getfem++ sources).

For example, the L2 norm of a field can be computed with:

gf_compute('L2 norm') or with:

gf_asm('volumic','u=data(#1); V()+=u(i).u(j).comp(Base(#1).Base(#1))(i,j)',mim,mf,U)

The Laplacian stiffness matrix can be evaluated with:

gf_asm('laplacian',mim, mf, A) or equivalently with:

gf_asm('volumic','a=data(#2);M(#1,#1)+=sym(comp(Grad(#1).Grad(#1).Base(#2))(:,i,:,i,j).a(j))', mim,mf, A);
asm_boundary(bnum, expr, mim=None, mf=None, data=None, *args)

Synopsis: (...) = asm_boundary(int bnum, string expr [, MeshIm mim, MeshFem mf, data...])

Generic boundary assembly.

See the help for gf_asm(‘volumic’).

asm_interpolation_matrix(mf, mfi)

Build the interpolation matrix from a MeshFem onto another MeshFem.

Return a matrix Mi, such that V = Mi.U is equal to gf_compute(‘interpolate_on’,mfi). Useful for repeated interpolations. Note that this is just interpolation, no elementary integrations are involved here, and mfi has to be lagrangian. In the more general case, you would have to do a L2 projection via the mass matrix.

Mi is a SpMat object.

asm_extrapolation_matrix(mf, mfe)

Build the extrapolation matrix from a MeshFem onto another MeshFem.

Return a matrix Me, such that V = Me.U is equal to gf_compute(‘extrapolate_on’,mfe). Useful for repeated extrapolations.

Me is a SpMat object.

Module compute

Various computations involving the solution U to a finite element problem.

compute_L2_norm(MF, U, mim, CVids=None)

Compute the L2 norm of the (real or complex) field U.

If CVids is given, the norm will be computed only on the listed convexes.

compute_H1_semi_norm(MF, U, mim, CVids=None)

Compute the L2 norm of grad(U).

If CVids is given, the norm will be computed only on the listed convexes.

compute_H1_norm(MF, U, mim, CVids=None)

Compute the H1 norm of U.

If CVids is given, the norm will be computed only on the listed convexes.

compute_H2_semi_norm(MF, U, mim, CVids=None)

Compute the L2 norm of D^2(U).

If CVids is given, the norm will be computed only on the listed convexes.

compute_H2_norm(MF, U, mim, CVids=None)

Compute the H2 norm of U.

If CVids is given, the norm will be computed only on the listed convexes.

compute_gradient(MF, U, mf_du)

Compute the gradient of the field U defined on MeshFem mf_du.

The gradient is interpolated on the MeshFem mf_du, and returned in DU. For example, if U is defined on a P2 MeshFem, DU should be evaluated on a P1-discontinuous MeshFem. mf and mf_du should share the same mesh.

U may have any number of dimensions (i.e. this function is not restricted to the gradient of scalar fields, but may also be used for tensor fields). However the last dimension of U has to be equal to the number of dof of mf. For example, if U is a [3x3xNmf] array (where Nmf is the number of dof of mf), DU will be a [Nx3x3[xQ]xNmf_du] array, where N is the dimension of the mesh, Nmf_du is the number of dof of mf_du, and the optional Q dimension is inserted if Qdim_mf != Qdim_mf_du, where Qdim_mf is the Qdim of mf and Qdim_mf_du is the Qdim of mf_du.

compute_hessian(MF, U, mf_h)

Compute the hessian of the field U defined on MeshFem mf_h.

See also gf_compute(‘gradient’, MeshFem mf_du).

compute_eval_on_triangulated_surface(MF, U, Nrefine, CVLIST=None)
[OBSOLETE FUNCTION! will be removed in a future release] Utility function designed for 2D triangular meshes : returns a list of triangles coordinates with interpolated U values. This can be used for the accurate visualization of data defined on a discontinous high order element. On output, the six first rows of UP contains the triangle coordinates, and the others rows contain the interpolated values of U (one for each triangle vertex) CVLIST may indicate the list of convex number that should be consider, if not used then all the mesh convexes will be used. U should be a row vector.
compute_interpolate_on(MF, U, *args)

Synopsis: Ui = compute_interpolate_on(MeshFem MF, vec U, {MeshFem mfi | Slice sli})

Interpolate a field on another MeshFem or a Slice.

  • Interpolation on another MeshFem mfi:

    mfi has to be Lagrangian. If mf and mfi share the same mesh object, the interpolation will be much faster.

  • Interpolation on a Slice sli:

    this is similar to interpolation on a refined P1-discontinuous mesh, but it is much faster. This can also be used with Slice(‘points’) to obtain field values at a given set of points.

See also gf_asm(‘interpolation matrix’)

compute_extrapolate_on(MF, U, mfe)

Extrapolate a field on another MeshFem.

If the mesh of mfe is stricly included in the mesh of mf, this function does stricly the same job as gf_compute(‘interpolate_on’). However, if the mesh of mfe is not exactly included in mf (imagine interpolation between a curved refined mesh and a coarse mesh), then values which are outside mf will be extrapolated.

See also gf_asm(‘extrapolation matrix’)

compute_error_estimate(MF, U, mim)

Compute an a posteriori error estimate.

Currently there is only one which is available: for each convex, the jump of the normal derivative is integrated on its faces.

compute_convect(MF, U, mf_v, V, dt, nt, option=None)
Compute a convection of U with regards to a steady state velocity field V with a Characteristic-Galerkin method. This method is restricted to pure Lagrange fems for U. mf_v should represent a continuous finite element method. dt is the integration time and nt is the number of integration step on the caracteristics. option is an option for the part of the boundary where there is a re-entrant convection. option = ‘extrapolation’ for an extrapolation on the nearest element or option = ‘unchanged’ for a constant value on that boundary. This method is rather dissipative, but stable.

Module delete

Delete an existing getfem object from memory (mesh, mesh_fem, etc.).

SEE ALSO:
gf_workspace, gf_mesh, gf_mesh_fem.
delete(I, J=None, K=None, *args)

Synopsis: delete(I[, J, K,...])

I should be a descriptor given by gf_mesh(), gf_mesh_im(), gf_slice() etc.

Note that if another object uses I, then object I will be deleted only when both have been asked for deletion.

Only objects listed in the output of gf_workspace(‘stats’) can be deleted (for example gf_fem objects cannot be destroyed).

You may also use gf_workspace(‘clear all’) to erase everything at once.

Module linsolve

Various linear system solvers.

linsolve_gmres(M, b, restart=None, *args)

Synopsis: X = linsolve_gmres(SpMat M, vec b[, int restart][, Mrecond P][,’noisy’][,’res’, r][,’maxiter’, n])

Solve M.X = b with the generalized minimum residuals method.

Optionally using P as preconditioner. The default value of the restart parameter is 50.

linsolve_cg(M, b, P=None, *args)

Synopsis: X = linsolve_cg(SpMat M, vec b [, Mrecond P][,’noisy’][,’res’, r][,’maxiter’, n])

Solve M.X = b with the conjugated gradient method.

Optionally using P as preconditioner.

linsolve_bicgstab(M, b, P=None, *args)

Synopsis: X = linsolve_bicgstab(SpMat M, vec b [, Mrecond P][,’noisy’][,’res’, r][,’maxiter’, n])

Solve M.X = b with the bi-conjugated gradient stabilized method.

Optionally using P as a preconditioner.

linsolve_lu(M, b)
Alias for gf_linsolve(‘superlu’,...)
linsolve_superlu(M, b)

Solve M.U = b apply the SuperLU solver (sparse LU factorization).

The condition number estimate cond is returned with the solution U.

Module poly

Performs various operations on the polynom POLY.

poly_print(P)
Prints the content of P.
poly_product(P)
To be done ... !

Module undelete

Undelete an existing getfem object from memory (mesh, mesh_fem, etc.).

SE ALSO: gf_workspace, gf_delete.
undelete(I, J=None, K=None, *args)

Synopsis: undelete(I[, J, K,...])

I should be a descriptor given by gf_mesh(), gf_mesh_im(), gf_slice() etc.

Module util

Performs various operations which do not fit elsewhere.

util_save_matrix(FMT, FILENAME, A)
Exports a sparse matrix into the file named FILENAME, using Harwell-Boeing (FMT=’hb’) or Matrix-Market (FMT=’mm’) formatting.
util_load_matrix(FMT, FILENAME)
Imports a sparse matrix from a file.
util_trace_level(level)

Set the verbosity of some getfem++ routines.

Typically the messages printed by the model bricks, 0 means no trace message (default is 3).

util_warning_level(level)

Filter the less important warnings displayed by getfem.

0 means no warnings, default level is 3.