Simple finite element assemblers
Project description
scikit-fem
scikit-fem
is a pure Python 3.8+ library for performing finite element
assembly. Its main
purpose is the transformation of bilinear forms into sparse matrices and linear
forms into vectors.
The library
- has minimal dependencies
- contains no compiled code
- supports one-dimensional, triangular, quadrilateral, tetrahedral and hexahedral finite elements
- includes special elements such as Raviart-Thomas, Nédélec, MINI, Crouzeix-Raviart, Argyris, ...
If you use the library in your research, you can cite the following article:
@article{skfem2020,
doi = {10.21105/joss.02369},
year = {2020},
volume = {5},
number = {52},
pages = {2369},
author = {Tom Gustafsson and G. D. McBain},
title = {scikit-fem: A {P}ython package for finite element assembly},
journal = {Journal of Open Source Software}
}
Installation
The most recent release can be installed simply by
pip install scikit-fem[all]
Remove [all]
to not install the optional dependencies meshio
for mesh
input/output, and matplotlib
for creating simple visualizations.
The minimal dependencies are numpy
and scipy
.
You can also try the library in browser through Google Colab.
Examples
Solve the Poisson problem (see also ex01.py
):
from skfem import *
from skfem.helpers import dot, grad
# create the mesh
mesh = MeshTri().refined(4)
# or, with your own points and elements:
# mesh = MeshTri(points, elements)
basis = Basis(mesh, ElementTriP1())
@BilinearForm
def laplace(u, v, _):
return dot(grad(u), grad(v))
@LinearForm
def rhs(v, _):
return 1. * v
A = laplace.assemble(basis)
b = rhs.assemble(basis)
# Dirichlet boundary conditions
A, b = enforce(A, b, D=mesh.boundary_nodes())
# solve the linear system
x = solve(A, b)
# plot using matplotlib
mesh.plot(x, shading='gouraud', colorbar=True).show()
# or, save to external file:
# mesh.save('output.vtk', point_data={'solution': x})
Meshes can be initialized manually, loaded from external files using meshio, or created with the help of special constructors:
import numpy as np
from skfem import MeshLine, MeshTri, MeshTet
mesh = MeshLine(np.array([0., .5, 1.]))
mesh = MeshTri(
np.array([[0., 0.],
[1., 0.],
[0., 1.]]).T,
np.array([[0, 1, 2]]).T,
)
mesh = MeshTri.load("docs/examples/meshes/square.msh") # requires meshio
mesh = MeshTet.init_tensor(*((np.linspace(0, 1, 60),) * 3))
We support many common finite elements. Below the stiffness matrix is assembled using second-order tetrahedra:
from skfem import Basis, ElementTetP2
basis = Basis(mesh, ElementTetP2()) # quadratic tetrahedron
A = laplace.assemble(basis) # type: scipy.sparse.csr_matrix
More examples can be found in the gallery.
Benchmark
The following benchmark (docs/examples/performance.py
) demonstrates the time
spent on finite element assembly in comparison to the time spent on linear
solve. The given numbers were calculated using a ThinkPad X1 Carbon laptop (7th
gen). Note that the timings are only illustrative as they depend on, e.g., the
type of element used, the number of quadrature points used, the type of linear
solver, and the complexity of the forms. This benchmark solves the Laplace
equation using linear tetrahedral elements and the default direct sparse solver
of scipy.sparse.linalg.spsolve
.
Degrees-of-freedom | Assembly (s) | Linear solve (s) |
---|---|---|
4096 | 0.04805 | 0.04241 |
8000 | 0.09804 | 0.16269 |
15625 | 0.20347 | 0.87741 |
32768 | 0.46399 | 5.98163 |
64000 | 1.00143 | 36.47855 |
125000 | 2.05274 | nan |
262144 | 4.48825 | nan |
512000 | 8.82814 | nan |
1030301 | 18.25461 | nan |
Documentation
The project is documented using Sphinx under docs/
.
Built version can be found from Read the Docs.
Here are direct links to additional resources:
Getting help
If you encounter an issue you can use GitHub issue tracker. If you cannot find help from the documentation, you can use the GitHub Discussions to ask questions. Try to provide a snippet of code which fails and include also the version of the library you are using. The version can be found as follows:
import skfem; print(skfem.__version__)
Dependencies
The minimal dependencies for installing scikit-fem
are
numpy and scipy. In addition,
many
examples use
matplotlib for visualization and
meshio for loading/saving different mesh
file formats. Some examples demonstrate the use of other external packages;
see requirements.txt
for a list of test dependencies.
Testing
The tests are run by GitHub Actions. The Makefile
in the repository root has
targets for running the testing container locally using docker
. For example,
make test_py38
runs the tests using py38
branch from
kinnala/scikit-fem-docker-action.
The releases are tested in
kinnala/scikit-fem-release-tests.
Licensing
The contents of skfem/
and the PyPI package scikit-fem
are licensed under
the 3-clause BSD license. Some examples under docs/examples/
or snippets
in the documentation may have a different license.
Acknowledgements
This project was started while working under a grant from the Finnish Cultural Foundation. Versions 2.0.0+ were prepared while working in a project funded by Academy of Finland (decisions nr. 324611 and 338341). The approach used in the finite element assembly has been inspired by the work of A. Hannukainen and M. Juntunen.
Contributing
We are happy to welcome any contributions to the library. Reasonable projects for first timers include:
- Reporting a bug
- Writing an example
- Improving the tests
- Suggesting improvements in the documentation.
By contributing code to scikit-fem, you are agreeing to release it under BSD-3-Clause, see LICENSE.md.
Changelog
The format is based on Keep a Changelog, and this project adheres to Semantic Versioning with respect to documented and/or tested features.
[10.0.1] - 2024-08-06
- Fixed:
Mesh.load
returned incorrect orientation for some Gmsh meshes with tagged interfaces
[10.0.0] - 2024-07-25
- Fixed:
Mesh.p2e
returned incorrect incidence - Fixed:
InteriorFacetBasis.get_dofs
did not return all edge DOFs for 3D elements - Added: The lowest order, one point integration rule for tetrahedral elements
- Added:
asm
will now wrap functions with three arguments usingBilinearForm
, functions with two arguments usingLinearForm
, etc. - Changed: Initializing
Basis
forElementTetP0
without specifyingintorder
orquadrature
will now automatically fall back to a one point integration rule - Changed: Default tags (left, right, top, ...) are no more
added automatically during mesh initialization, as a workaround you
can add them explicitly by calling
mesh = mesh.with_defaults()
- Changed: All indices within the library are now using
np.int32
for around 10% boost in performance and the corresponding reduction in memory usage for larger meshes - theoretically, the largest possible tetrahedral tensor product mesh is now roughly 550 ** 3 = 166 M vertices and 993 M elements, without the facet indexing wrapping over 2 ** 32
[9.1.1] - 2024-04-23
- Fixed: Tests now pass with
numpy==2.0rc1
- Fixed:
MappingAffine
now uses lazy evaluation also for element mappings, in addition to boundary mappings - Fixed:
MeshTet.init_tensor
uses significantly less memory for large meshes - Fixed:
Mesh.load
uses less memory when loading and matching tags - Added:
Basis
has new optionaldisable_doflocs
kwarg which can be set toTrue
to avoid computingBasis.doflocs
, to reduce memory usage
[9.0.1] - 2024-01-12
- Fixed:
ElementVector
now works also for split_bases/split_indices in casemesh.dim() != elem.dim
[9.0.0] - 2023-12-24
- Removed: Python 3.7 support
- Removed:
MappingMortar
andMortarFacetBasis
in favor ofskfem.supermeshing
- Deprecated:
skfem.visuals.glvis
; current version is broken and no replacement is being planned - Added: Python 3.12 support
- Added:
Mesh.load
supports new keyword argumentsignore_orientation=True
andignore_interior_facets=True
which will both speed up the loading of larger three-dimensional meshes by ignoring facet orientation and all tags not on the boundary, respectively. - Added:
skfem.supermeshing
(requiresshapely>=2
) for creating quadrature rules for interpolating between two 1D or 2D meshes. - Added:
Mesh.remove_unused_nodes
- Added:
Mesh.remove_duplicate_nodes
- Added:
Mesh.remove_elements
now supports passing any subdomain reference throughMesh.normalize_elements
; subdomains and boundaries are also properly preserved - Fixed:
MeshTet
uniform refine was reindexing subdomains incorrectly - Fixed:
MeshDG.draw
did not work; now callsBasis.draw
which works for any mesh topology - Fixed:
FacetBasis
now works withMeshTri2
,MeshQuad2
,MeshTet2
andMeshHex2
- Fixed:
ElementGlobal
now uses outward normals to initialize DOFs on boundary facets
[8.1.0] - 2023-06-16
- Added:
ElementTriHHJ0
andElementTriHHJ1
matrix finite elements for implementing the Hellan-Hermann-Johnson mixed method (seeex48.py
) - Added:
ElementHexSkeleton0
, piecewise constant element on the skeleton of a hexahedral mesh - Added:
ElementHexC1
, C1-continuous hexahedral element - Added:
Mesh.restrict
now preserves subdomains and boundaries - Added:
skfem.utils.mpc
for setting multipoint constraints - Added:
Basis.get_dofs
now supports fetching DOFs at specific nodes through kwargnodes
- Added:
DofsView.sort
for sorting a set of DOFs returned byBasis.get_dofs
- Added:
CellBasis.with_elements
as a shortcut for initiating a new Basis with subset of elements - Added:
Mesh.refined
now preserves subdomains in adaptive mesh refinement - Fixed:
Mesh.refined
used to modify the element connectivity of the original mesh
[8.0.0] - 2022-12-16
- Removed: The deprecated
Basis.find_dofs
method, seeBasis.get_dofs
for a replacement - Added: Renamed
ElementTetN0
toElementTriN1
and added alias for backwards compatibility - Added:
ElementQuadN1
, first order H(curl) conforming quadrilateral element - Added:
ElementTriN1
, first order H(curl) conforming triangle element - Added:
ElementTriN2
, second order H(curl) conforming triangle element - Added:
ElementTetSkeletonP0
, extension ofElementTriSkeletonP0
to tetrahedral meshes - Added:
Mesh.restrict
which returns a new mesh given a subset of elements or subdomain - Added:
Mesh.trace
which turns facets into a trace mesh - Added:
skfem.utils.bmat
, a variant ofscipy.sparse.bmat
which adds the indices of the different blocks as an attributeout.blocks
- Added: Plane strain to plane stress mapping under
skfem.models.elasticity
- Added: Various methods such as
Basis.interpolate
andBasis.project
now support specifyingdtype
and using complex fields - Fixed: Python 3.11
- Fixed:
Basis.intepolate
did not work properly withElementComposite
when the basis was defined only for a subset of elements - Fixed:
Basis.split
worked incorrectly forElementVector
and multiple DOFs of same type - Fixed: Caching of
ElementQuadP
basis for reused quadrature points did not work correctly - Deprecated:
MappingMortar
andMortarFacetBasis
in favor of plainFacetBasis
and the upcomingskfem.experimental.supermeshing
(seeex04.py
)
[7.0.1] - 2022-08-03
- Fixed: Updated changelog was missing.
[7.0.0] - 2022-08-03
- Changed: Removed the optimization of using
DiscreteField.is_zero
in the helpers to skip the evaluation of zero components inElementComposite
to improve type stability with respect to the size of the underlying numpy arrays; this is technically a backwards incompatible change and might affect self-created helper functions - Deprecated:
FacetBasis.trace
in favor ofBasis.interpolator
andBasis.project
- Added: Output of
Basis.interpolator
supports trailing axes; can be now passed toBasis.project
for (inexact) interpolation between meshes - Added: Renamed
ElementTriRT0
toElementTriRT1
and added alias for backwards compatibility - Added: Renamed
ElementTetRT0
toElementTetRT1
and added alias for backwards compatibility - Added: Renamed
ElementQuadRT0
toElementQuadRT1
and added alias for backwards compatibility - Added:
ElementTriRT2
, the second order Raviart-Thomas element - Added:
ElementHexRT1
, the first order Raviart-Thomas element for hexahedral meshes - Added:
Basis.project
now better supportsElementComposite
- Added:
solver_iter_cg
, a simple pure Python conjugate gradient solver for environments that do not have sparse solver libraries (e.g., Pyodide) - Added:
ElementTriP2B
andElementTriP1B
, new aliases forElementTriMini
andElementTriCCR
- Added:
ElementTriP1G
andElementTriP2G
, variants ofElementTriP1
andElementTriP2
usingElementGlobal
so that second derivatives are available (useful, e.g., for stabilized methods and the Stokes problem) - Added:
Basis.plot3
, a wrapper toskfem.visuals.*.plot3
- Fixed: Calculation of size in
Basis.__repr__
was slow and incorrect - Fixed: Subclasses of
ElementHdiv
did not work together withFacetBasis
[6.0.0] - 2022-03-15
- Changed:
DiscreteField
is now a subclass ofndarray
instead ofNamedTuple
and, consequently, the components ofDiscreteField
cannot no more be indexed inside forms likeu[1]
(useu.grad
instead) - Changed: Writing
w['u']
andw.u
inside the form definition is now equivalent (previouslyw.u == w['u'].value
) - Changed:
Mesh.draw
now usesmatplotlib
by default, callingMesh.draw("vedo")
usesvedo
- Changed:
skfem.visuals.matplotlib
now usesjet
as the default colormap - Changed:
BoundaryFacetBasis
is now an alias ofFacetBasis
instead of other way around - Deprecated:
DiscreteField.value
remains for backwards-compatibility but is now deprecated and can be dropped - Added:
Mesh.plot
, a wrapper toskfem.visuals.*.plot
- Added:
Basis.plot
, a wrapper toskfem.visuals.*.plot
- Added:
Basis.refinterp
now supports vectorial fields - Added:
skfem.visuals.matplotlib.plot
now has a basic quiver plot for vector fields - Added:
Mesh.facets_around
which constructs a set of facets around a subdomain - Added:
Mesh.save
andload
now preserve the orientation of boundaries and interfaces - Added:
OrientedBoundary
which is a subclass ofndarray
for facet index arrays with the orientation information (0 or 1 per facet) available asOrientedBoundary.ori
- Added:
FacetBasis
will use the facet orientations (if present) to calculate traces and normal vectors - Added:
skfem.visuals.matplotlib.draw
will visualize the orientations ifboundaries=True
is given - Added:
Mesh.facets_satisfying
allows specifying the keyword argumentnormal
for orienting the resulting interface - Added:
FacetBasis
constructor now has the keyword argumentside
which allows changing the side of the facet used to calculate the basis function values and gradients - Added:
Basis.boundary
method to quickly initialize the correspondingFacetBasis
- Fixed: Improvements to backwards compatibility in
asm
/assemble
keyword arguments - Fixed: Save format issue with meshio 5.3.0+
- Fixed:
CellBasis
did not properly supportelements
argument - Fixed:
Basis.interpolate
did not properly interpolate all components ofElementComposite
[5.2.0] - 2021-12-27
- Added:
Basis.project
, a more general and easy to use alternative forprojection
- Added:
Basis
andFacetBasis
kwargselements
andfacets
can now be a string refering to subdomain and boundary tags - Added:
ElementQuadRT0
, lowest-order quadrilateral Raviart-Thomas element - Fixed:
Functional
returned only the first component for forms with non-scalar output
[5.1.0] - 2021-11-30
- Added:
skfem.helpers.mul
for matrix multiplication - Added:
Basis.split
will now also splitElementVector
into its components - Fixed:
ElementDG
was not included in the wildcard import - Fixed: Automatic visualization of
MeshTri2
andMeshQuad2
in Jupyter notebooks raised exception
[5.0.0] - 2021-11-21
- Changed:
meshio
is now an optional dependency - Changed:
ElementComposite
usesDiscreteField()
to represent zero - Added: Support more argument types in
Basis.get_dofs
- Added: Version information in
skfem.__version__
- Added: Preserve
Mesh.boundaries
during uniform refinement ofMeshLine1
,MeshTri1
andMeshQuad1
- Fixed: Refinement of quadratic meshes will now fall back to the refinement algorithm of first-order meshes instead of crashing
- Fixed: Edge cases in the adaptive refine of
MeshTet1
that failed to produce a valid mesh - Deprecated:
Basis.find_dofs
in favor ofBasis.get_dofs
- Deprecated: Merging
DofsView
objects via+
and|
because of surprising behavior in some edge cases
[4.0.1] - 2021-10-15
- Fixed:
MappingIsoparametric
can now be pickled
[4.0.0] - 2021-09-27
- Added:
Mesh.save
/Mesh.load
now exports/importsMesh.subdomains
andMesh.boundaries
- Added:
Mesh.load
now optionally writes any mesh data to a list passed via the keyword argumentout
, e.g.,out=data
wheredata = ['point_data']
- Added:
Mesh.load
(andskfem.io.meshio.from_file
) now supports the additional keyword argumentforce_meshio_type
for loading mesh files that have multiple element types written in the same file, one element type at a time - Added:
asm
will now accept a list of bases, assemble the same form using all of the bases and sum the result (useful for jump terms and mixed meshes, seeex41.py
- Added:
Mesh.with_boundaries
now allows the definition of internal boundaries/interfaces via the flagboundaries_only=False
- Added:
MeshTri1DG
,MeshQuad1DG
,MeshHex1DG
,MeshLine1DG
; new mesh types for describing meshes with a discontinuous topology, e.g., periodic meshes (seeex42.py
) - Added:
ElementHexDG
for transforming hexahedral H1 elements to DG/L2 elements. - Added:
ElementTriP1DG
,ElementQuad1DG
,ElementHex1DG
,ElementLineP1DG
; shorthands forElementTriDG(ElementTriP1())
etc. - Added:
ElementTriSkeletonP0
andElementTriSkeletonP1
for defining Lagrange multipliers on the skeleton mesh (seeex40.py
) - Added:
TrilinearForm
for assembling a sparse 3-tensor, e.g., when dealing with unknown material data - Added:
MeshTri.oriented
for CCW oriented triangular meshes which can be useful for debugging or interfacing to external tools - Added: partial support for
MeshWedge1
andElementWedge1
, the lowest order wedge mesh and element - Added:
ElementTriP3
, cubic triangular Lagrange element - Added:
ElementTriP4
, quartic triangular Lagrange element - Added:
ElementTri15ParamPlate
, 15-parameter nonconforming triangular element for plates - Added:
ElementTriBDM1
, the lowest order Brezzi-Douglas-Marini element - Added:
Mesh.draw().show()
will now visualize any mesh interactively (requires vedo) - Added: Adaptive refinement for
MeshTet1
- Fixed:
MappingIsoparametric
is now about 2x faster for large meshes thanks to additional caching - Fixed:
MeshHex2.save
did not work properly - Fixed:
Mesh.load
ignores unparseablecell_sets
inserted bymeshio
in MSH 4.1 - Changed:
Mesh
string representation is now more informative - Changed:
Form.assemble
no more allows keyword arguments withlist
ordict
type: from now on onlyDiscreteField
or 1d/2dndarray
objects are allowed and 1dndarray
is passed automatically toBasis.interpolate
for convenience - Changed:
MeshLine
is now a function which initializesMeshLine1
and not an alias toMeshLine1
- Changed:
FacetBasis
is now a shorthand forBoundaryFacetBasis
and no longer initializesInteriorFacetBasis
orMortarFacetBasis
if the keyword argumentside
is passed to the constructor - Removed: the deprecated
Mesh.define_boundary
method
[3.2.0] - 2021-08-02
- Added:
ElementTriCCR
andElementTetCCR
, conforming Crouzeix-Raviart finite elements - Fixed:
Mesh.mirrored
returned a wrong mesh when a point other than the origin was used - Fixed:
MeshLine
constructor accepted only numpy arrays and not plain Python lists - Fixed:
Mesh.element_finder
(andCellBasis.probes
,CellBasis.interpolator
) was not working properly for a small number of elements (<5) or a large number of input points (>1000) - Fixed:
MeshTet
andMeshTri.element_finder
are now more robust against degenerate elements - Fixed:
Mesh.element_finder
(andCellBasis.probes
,CellBasis.interpolator
) raises exception if the query point is outside of the domain
[3.1.0] - 2021-06-18
- Added:
Basis
, a shorthand forCellBasis
- Added:
CellBasis
, a new preferred name forInteriorBasis
- Added:
BoundaryFacetBasis
, a new preferred name forExteriorFacetBasis
- Added:
skfem.utils.penalize
, an alternative tocondense
andenforce
for essential boundary conditions - Added:
InteriorBasis.point_source
, withex38
- Added:
ElementTetDG
, similar toElementTriDG
for tetrahedral meshes - Fixed:
MeshLine1.element_finder
[3.0.0] - 2021-04-19
- Added: Completely rewritten
Mesh
base class which is "immutable" and usesElement
classes to define the ordering of nodes; better support for high-order and other more general mesh types in the future - Added: New quadratic mesh types:
MeshTri2
,MeshQuad2
,MeshTet2
andMeshHex2
- Added:
InteriorBasis.probes
; likeInteriorBasis.interpolator
but returns a matrix that operates on solution vectors to interpolate them at the given points - Added: More overloads for
DiscreteField
, e.g., multiplication, summation and subtraction are now explicitly supported inside the form definitions - Added:
MeshHex.to_meshtet
for splitting hexahedra into tetrahedra - Added:
MeshHex.element_finder
for interpolating finite element solutions on hexahedral meshes viaInteriorBasis.interpolator
- Added:
Mesh.with_boundaries
, a functional replacement toMesh.define_boundary
, i.e. defining boundaries via Boolean lambda function - Added:
Mesh.with_subdomains
for defining subdomains via Boolean lambda function - Added:
skfem.utils.projection
, a replacement ofskfem.utils.project
with a different, more intuitive order of arguments - Added:
skfem.utils.enforce
for setting essential boundary conditions by changing matrix rows to zero and diagonals to one. - Deprecated:
skfem.utils.project
in favor ofskfem.utils.projection
- Deprecated:
Mesh.define_boundary
in favor ofMesh.with_boundaries
- Removed:
Mesh.{refine,scale,translate}
; the replacements areMesh.{refined,scaled,translated}
- Removed:
skfem.models.helpers
; available asskfem.helpers
- Removed:
DiscreteField.{f,df,ddf,hod}
; available asDiscreteField.{value,grad,hess,grad3,...}
- Removed: Python 3.6 support
- Removed:
skfem.utils.L2_projection
- Removed:
skfem.utils.derivative
- Changed:
Mesh.refined
no more attempts to fix the indexing ofMesh.boundaries
after refine - Changed:
skfem.utils.solve
now usesscipy.sparse.eigs
instead ofscipy.sparse.eigsh
by default; the old behavior can be retained by explicitly passingsolver=solver_scipy_eigs_sym()
- Fixed: High memory usage in
skfem.visuals.matplotlib
related to 1D plotting
[2.5.0] - 2021-02-13
- Deprecated:
side
keyword argument toFacetBasis
in favor of the more explicitInteriorFacetBasis
andMortarFacetBasis
. - Added:
InteriorFacetBasis
for integrating over the interior facets, e.g., evaluating error estimators with jumps and implementing DG methods. - Added:
MortarFacetBasis
for integrating over the mortar mesh. - Added:
InteriorBasis.with_element
for reinitializing an equivalent basis that uses a different element. - Added:
Form.partial
for applyingfunctools.partial
to the form function wrapped byForm
. - Fixed: Include explicit Python 3.9 support.
[2.4.0] - 2021-01-20
- Deprecated: List and tuple keyword argument types to
asm
. - Deprecated:
Mesh2D.mirror
in favor of the more generalMesh.mirrored
. - Deprecated:
Mesh.refine
,Mesh.scale
andMesh.translate
in favor ofMesh.refined
,Mesh.scaled
andMesh.translated
. - Added:
Mesh.refined
,Mesh.scaled
, andMesh.translated
. The new methods return a copy instead of modifyingself
. - Added:
Mesh.mirrored
for mirroring a mesh using a normal and a point. - Added:
Functional
now supports forms that evaluate to vectors or other tensors. - Added:
ElementHex0
, piecewise constant element for hexahedral meshes. - Added:
FacetBasis.trace
for restricting existing solutions to lower dimensional meshes on boundaries or interfaces. - Fixed:
MeshLine.refined
now correctly performs adaptive refinement of one-dimensional meshes.
[2.3.0] - 2020-11-24
- Added:
ElementLineP0
, one-dimensional piecewise constant element. - Added:
skfem.helpers.curl
now calculates the rotated gradient for two-dimensional elements. - Added:
MeshTet.init_ball
for meshing a ball. - Fixed:
ElementQuad0
was not compatible withFacetBasis
.
[2.2.3] - 2020-10-16
- Fixed: Remove an unnecessary dependency.
[2.2.2] - 2020-10-15
- Fixed: Make the preconditioner in
TestEx32
more robust.
[2.2.1] - 2020-10-15
- Fixed: Remove
tests
from the PyPI distribution.
[2.2.0] - 2020-10-14
- Deprecated:
L2_projection
will be replaced byproject
. - Deprecated:
derivative
will be replaced byproject
. - Added:
MeshTet.element_finder
andMeshLine.element_finder
for usingInteriorBasis.interpolator
. - Added:
ElementTriCR
, the nonconforming Crouzeix-Raviart element for Stokes flow. - Added:
ElementTetCR
, tetrahedral nonconforming Crouzeix-Raviart element. - Added:
ElementTriHermite
, an extension ofElementLineHermite
to triangular meshes. - Fixed: Fix
Mesh.validate
for unsignedMesh.t
.
[2.1.1] - 2020-10-01
- Fixed: Further optimizations to
Mesh3D.boundary_edges
: tested to run on a laptop with over 10 million elements.
[2.1.0] - 2020-09-30
- Added:
ElementHex2
, a triquadratic hexahedral element. - Added:
MeshTri.init_circle
, constructor for a circle mesh. - Fixed:
Mesh3D.boundary_edges
(and, consequently,Basis.find_dofs
) was slow and used lots of memory due to an exhaustive search of all edges.
[2.0.0] - 2020-08-21
- Deprecated:
project
will only support functions likelambda x: x[0]
instead oflambda x, y, z: x
in the future. - Added: Support for complex-valued forms:
BilinearForm
andLinearForm
now take an optional argumentdtype
which defaults tonp.float64
but can be alsonp.complex64
. - Added:
Dofs.__or__
andDofs.__add__
, for merging degree-of-freedom sets (i.e.Dofs
objects) using|
and+
operators. - Added:
Dofs.drop
andDofs.keep
, for further filtering the degree-of-freedom sets - Removed: Support for old-style decorators
bilinear_form
,linear_form
, andfunctional
(deprecated since 1.0.0). - Fixed:
FacetBasis
did not initialize withElementQuadP
.
[1.2.0] - 2020-07-07
- Added:
MeshQuad._splitquads
aliased asMeshQuad.to_meshtri
. - Added:
Mesh.__add__
, for merging meshes using+
operator: duplicated nodes are joined. - Added:
ElementHexS2
, a 20-node quadratic hexahedral serendipity element. - Added:
ElementLineMini
, MINI-element for one-dimensional mesh. - Fixed:
Mesh3D.boundary_edges
was broken in case of hexahedral meshes. - Fixed:
skfem.utils.project
did not work forElementGlobal
.
[1.1.0] - 2020-05-18
- Added:
ElementTetMini
, MINI-element for tetrahedral mesh. - Fixed:
Mesh3D.boundary_edges
incorrectly returned all edges where both nodes are on the boundary.
[1.0.0] - 2020-04-22
- Deprecated: Old-style form constructors
bilinear_form
,linear_form
, andfunctional
. - Changed:
Basis.interpolate
returnsDiscreteField
objects instead of ndarray tuples. - Changed:
Basis.interpolate
works now properly for vectorial and high-order elements by interpolating all components and higher order derivatives. - Changed:
Form.assemble
accepts now any keyword arguments (with typeDiscreteField
) that are passed over to the forms. - Changed: Renamed
skfem.importers
toskfem.io
. - Changed: Renamed
skfem.models.helpers
toskfem.helpers
. - Changed:
skfem.utils.solve
will now expand also the solutions of eigenvalue problems. - Added: New-style form constructors
BilinearForm
,LinearForm
, andFunctional
. - Added:
skfem.io.json
for serialization of meshes to/from json-files. - Added:
ElementLinePp
, p-th order one-dimensional elements. - Added:
ElementQuadP
, p-th order quadrilateral elements. - Added:
ElementQuadDG
for transforming quadrilateral H1 elements to DG elements. - Added:
ElementQuadBFS
, Bogner-Fox-Schmit element for biharmonic problems. - Added:
ElementTriMini
, MINI-element for Stokes problems. - Added:
ElementComposite
for using multiple elements in one bilinear form. - Added:
ElementQuadS2
, quadratic Serendipity element. - Added:
ElementLineHermite
, cubic Hermite element for Euler-Bernoulli beams. - Added:
Mesh.define_boundary
for defining named boundaries. - Added:
Basis.find_dofs
for finding degree-of-freedom indices. - Added:
Mesh.from_basis
for defining high-order meshes. - Added:
Basis.split
for splitting multicomponent solutions. - Added:
MortarMapping
with basic support for mortar methods in 2D. - Added:
Basis
constructors now acceptquadrature
keyword argument for specifying a custom quadrature rule.
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