firedrakeproject / fiat

This is FIAT. FIAT was previously maintained as part of the FEniCS project (https://github.com/fenics/fiat)

FIAT: FInite element Automatic Tabulator

The FInite element Automatic Tabulator FIAT supports generation of arbitrary order instances of the Lagrange elements on lines, triangles, and tetrahedra. It is also capable of generating arbitrary order instances of Jacobi-type quadrature rules on the same element shapes. Further, H(div) and H(curl) conforming finite element spaces such as the families of Raviart-Thomas, Brezzi-Douglas-Marini and Nedelec are supported on triangles and tetrahedra. Upcoming versions will also support Hermite and nonconforming elements.

FIAT is part of the FEniCS Project.

For more information, visit http://www.fenicsproject.org

Documentation

Documentation can be viewed at http://fenics-fiat.readthedocs.org/.

License

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.

fiat's Issues

need a pyproject.toml

setup.py is obsolete and the specific contents are hilariously out of date.

Borked H(div) trace tabulation when asking for derivatives

import FIAT
from FIAT.reference_element import UFCTetrahedron

elem = FIAT.HDivTrace(UFCTetrahedron(), 0)
print elem.tabulate(1, [[1./3, 1./3]], entity=(2, 0))

prints:

{(1, 0, 0): TraceError('Gradient evaluations are illegal on trace elements.',),
 (0, 1, 0): TraceError('Gradient evaluations are illegal on trace elements.',),
 (0, 0, 0): TraceError('Gradient evaluations are illegal on trace elements.',),
 (0, 0, 1): array([[ 1.],
       [ 0.],
       [ 0.],
       [ 0.]])}

Non-equispaced Lagrange elements on simplices

If we want to implement simplicial Lagrange elements with the recursive nodes from https://epubs.siam.org/doi/pdf/10.1137/20M1321802, should we implement them as a new class or could they be the extension of the 1D elements (GaussLegendre and GaussLobattoLegendre) that we already have?

FIAT reluctant to create high-order quadrature rules

Because of this sanity check. However, high order quadrature degrees are completely legitimate when solving for high-order discretisations. @wence-: what should we do?

Taylor basis for triangles

Currently DiscontinuousTaylor class only supports interval elements.

More Lagrange variants

1. Should we have a single base class for Lagrange and DiscontinuousLagrange?

2. If we want equispaced and GL variants of Discontinuous Lagrange, we need to change the current topological DOF ordering of DiscontinousLagrange, as there are no GL points on facets.

3. GaussRadau should subclass Lagrange, but these nodes are not available in recursivenodes.

Refactoring functionals

It seems like our code would be a lot cleaner if we could have sets of functionals (the gradient at a point, in Cartesian or tangent/normal coordinates, moments against all polynomials of some degree on a facet, etc).

Advantages:

• Easier implementation of elements
• Easier to batch together the evaluations in to_riesz
• Possibly easier inference of zany mappings in FInAT (hypothesized).

Challenges:

• This is a pervasive change in functional.py and may require reimplementing all our Ciarlet finite elements
• We need to make sure not to bump anything indirectly (e.g. code generation of general interpolation operators)