pyxfem.core.function_spaces module

Created on Mon Dec 4 23:30:08 2023

@author: nchevaug

class pyxfem.core.function_spaces.DofManagerBase

Bases: ABC

Base class to help manage degree of freedoms

edge2edgeid(e2v, getxy=False)

from edge defined by there vertices id, recover the edgeid as seen by the space

edgeid2dofid(edges)

from edge id recover the associated dofid For FEMSpaceP1, return an empty array

scalar_size()

size (nbdofs) for a scalar space

size()

size (nbdofs) taking into account the vector dim of the field

vertexid2dofid(vids)

return the dofs number associated to the vertices id

class pyxfem.core.function_spaces.FEMSpaceP1(name: str, mesh: SMesh, vecdim: int = 1, tris_map: None | MappingT3 = None)

Bases: object

Classical Linear Finite Element space

static N(uv)

Shape function for the triangle

dNdu = array([[-1.,  1.,  0.],        [-1.,  0.,  1.]])

edge2edgeid(e2v, getxy=False)

from edge defined by there vertices id, recover the edgeid as seen by the space

edgeid2dofid(edges)

from edge id recover the associated dofid For FEMSpaceP1, return an empty array

get_tris_mapping()

return the (linear mapping (see mapping.MappingT3)) of the mesh entities

interpolate(f)

interpolate the function f on to mesh nodes

interpolatoryAt = 'vertex'

lenN = 3

operator_dof2grad_tri(evaltrisuv, rmap=None, frmap=None, only_on=None, raw_data=False, limited=False)

Return operator dNdx that map the dof value to the gradient of field values at each point uv for each triangle

operator_dof2val_edge(eids, evaledge_s=array([0.5]))

Return operator N that map the dof value to the field values at each point s of each edge

operator_dof2val_tri(evaltris_uv, rmap=None, frmap=None, only_on=None, raw_data=False)

Return operator N that map the dof value to the field values at each point uv for each triangle

scalar_size()

size (nbdofs) for a scalar space

size()

size (nbdofs) taking into account the vector dim of the field

vertexid2dofid(vids)

return the dofs number associated to the vertices id

class pyxfem.core.function_spaces.FEMSpaceP1NC(name, mesh: SMesh, vecdim=1, tris_map=None)

Bases: object

Implementation of cruzeix-raviart Element

static N(uv)

Shape function for the triangle

dNdu = array([[ 0.,  2., -2.],        [-2.,  2.,  0.]])

edge2dofid(e2v)

from edge defined by there vertices id, return the associated dofs

edge2edgeid(e2v, getxy=False)

from edge defined by there vertices id, recover the edgeid as seen by the space

edgeid2dofid(eidspace)

from edge id recover the associated dofid

get_tris_mapping()

return the (linear mapping (see mapping.MappingT3)) of the mesh entities

interpolate(f) → NDArray[float64]

Compute values of u dofs so that Ni*ui is equal to f at mid edge

interpolatoryAt = 'midEdge'

lenN = 3

operator_dof2grad_tri(evaltrisuv, rmap=None, frmap=None, only_on=None, raw_data=False, limited=False)

Return operator dNdx that map the dof value to the gradient of field values at each point uv for each triangle

operator_dof2val_edge(eids, evaledges=array([0.5]))

Return operator N that map the dof value to the field values at each point s of each edge

operator_dof2val_tri(evaltrisuv, rmap=None, frmap=None, only_on=None, raw_data=False)

Return operator N that map the dof value to the field values at each point uv for each triangle

operator_edgetrace(quad_edges)

return a linear sparse operator N that compute the trace on each edge at points quad_edges from the dof values. t = N@U is an np.array for size nedge*npt*vecdim*2 (it that order) the entries i,j k of t.reshape((nedge, npt, vecdim, 2)) contain the 2 value at edge i, point j, direction k, which correspond to the values at left and right of the edge (we assume here a 2d manifold)

operator_trival2edge(ndata_per_edge=None, data_size=1)

return linear operator that push values at triangles to each edge. useful to compute interelemnt jump for example

scalar_size()

size (nbdofs) for a scalar space

size()

size (nbdofs) taking into account the vector dim of the field

vertexid2dofid(vids)

return the dofs number associated to the vertices id

class pyxfem.core.function_spaces.Heaviside(name, mesh_cut_data, ls_tris, ls_tris_cut)

Bases: object

Heaviside shape function defined on a cut mesh

eval(evaltrisuv, only_on_parents=None, frmap=None)

evaluate the function at each point uv of each element or sub element

class pyxfem.core.function_spaces.LinearScalarField(a=3, b=4)

Bases: object

A linear field in 2d : u(x,y) = a*x + b*y

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.LinearVectorField

Bases: object

an example of Vector field for test purpose

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.QuadraticScalarField(hess=array([[1., 0.], [0., 1.]]))

Bases: object

A Quadratic field for example purpose

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.QuadraticVectorField

Bases: object

an example of Vector field for test purpose

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.Ridge(name, mesh_cut_data, ls_tris, ls_tris_cut)

Bases: object

Ridge shape function defined on a cut mesh (usefull for discontinuous gradient)

eval(evaltrisuv, only_on_parents=None, frmap=None, raw_data=False)

evaluate the function at each point uv of each element or sub element

evalGrad(evaltrisuv, only_on_parents=None, frmap=None)

evaluate the gradiant of thefunction at each point uv of each element or sub element

class pyxfem.core.function_spaces.SomeScalarField(f=1.0)

Bases: object

an example of scalar field for test purpose

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.SomeVectorField(f)

Bases: object

an example of vector field for test purpose

fun(xy)

eval the function at points xy

grad(xy)

eval the gradient of function at points xy

class pyxfem.core.function_spaces.SumSpace(list_of_space)

Bases: object

make a space as a sum of different space

operator_dof2grad_tri(evaltrisuv, rmap=None)

Return operator dNdx that map the dof value to the gradient of field values at each point uv for each triangle

operator_dof2val_tri(evaltrisuv, rmap=None)

Return operator N that map the dof value to the field values at each point uv for each triangle

class pyxfem.core.function_spaces.TestSparseOp(methodName='runTest')

Bases: TestCase

Class for unit test of operator on dofs

test_operator_trival2edge()

Test of the operator tha push triangles data to edges

class pyxfem.core.function_spaces.VertexSpaceDofManager(m: SMesh, vecdim=3)

Bases: object

Class to compute the degree of freedom associated to the mesh and the dirichlet BC

size()

Return the total size of the space (number of (scalar) dof in the space )

vertexid2dofid(vids)

return an array A of shape (nv, vecdim) containing such as A[i, j] is the de index of degree of freedom associated to node i in vector direction j

class pyxfem.core.function_spaces.XFEMSpace(name, basespace, enrichment, mesh_cut, ls, ls_cut, rmap=None)

Bases: object

XFEM Function space : input an enrichment function and a base space and a level set on which the enrichment is defined

operator_dof2grad_tri(evaltrisuv, rmap=None)

Return operator dNdx that map the dof value to the gradient of field values at each point uv for each triangle

operator_dof2val_tri(evaltrisuv, rmap=None)

Return operator N that map the dof value to the field values at each point uv for each triangle

scalar_size()

size (nbdofs) for a scalar space

class pyxfem.core.function_spaces.XRidgeSpaceP1(name, mesh_cut, ls, ls_cut, rmap=None, dosvd=False)

Bases: object

A special enrichment space for Ridge enrichment

operator_dof2grad_tri(evaltrisuv, rmap=None)

Return operator dNdx that map the dof value to the gradient of field values at each point uv for each triangle

operator_dof2val_tri(evaltrisuv, rmap=None, raw=False)

Return operator N that map the dof value to the field values at each point uv for each triangle

scalar_size()

size (nbdofs) for a scalar space

pyxfem.core.function_spaces.gradNTri(dNdu, uv, invF)

Compute the gradient with regard to space coordinates xy from gradient with regard to element coordinate uv

pyxfem.core.function_spaces.meshcutdata2remap_helper(mesh_cut, hmin=0.0, alpha=0.1, p=1)

build a RemapHelper Object from mesh_cut data

pyxfem.core.function_spaces.op2sparse(NScalar, nscalar_dofs, a2scalardofs, vecdim, nshapeperelem, nptperelem, ndataperpoint, only_on=None)

Given a N array (shape function values at integration point for each element and numbering of degree of freedom dat, construct the sparse N Operator (Assembly)

pyxfem.core.function_spaces.op2sparse_rmap(NScalar, nscalar_dofs, a2scalardofs, vecdim, nshapeperelem, nptperelem, ndataperpoint, rmap, frmap=None, sort=True)

Given a N array (shape function values at integration point for each element (or sub element)) and numbering of degree of freedom dat, construct the sparse N Operator (Assembly) Specialized version for the case (typically xfem) where element are cut in sub cell

pyxfem.core.function_spaces.operator_dof2grad_tri(space, vecdim, geomdim, scalar_space_size, tri2dofs, trimap, evaltrisuv, rmap=None, frmap=None, only_on=None, raw_data=False, limited=False)

helper function : return operator N that map the dof value to the gradient of field values at each point uv for each triangle

pyxfem.core.function_spaces.operator_dof2value(space, vecdim, scalar_space_size, tri2dofs, evaltrisuv, rmap=None, frmap=None, raw_data=False, only_on=None)

return a linear operator N that map dof value to value at interpolation point of each element

pyxfem.core.function_spaces.operator_trival2edge(nedge, t2e, t2eflip, ndataperedge=None, datasize=1, dtype=<class 'numpy.float64'>)

return linear operator that push values at triangles to each edge. useful to compute interelemnt jump for example