Glossary

UFL

The Unified Form Language. Documentation at: https://docs.fenicsproject.org/ufl/main/

FFCx

The FEniCSx Form Compiler. Documentation at: https://docs.fenicsproject.org/ffcx/main/

DOLFINx

The user-interface of the FEniCS project. Documentation at: https://docs.fenicsproject.org/dolfinx/main/

FEM

The Finite Element Method

FE

A finite element. A encyclopedia can be found at: https://defelement.com/

Tabulation

Filling a n-th order tensor with data. Term often used when computing basis values and derivatives at a set of points.

Assemble

Integrate a compiled DOLFINx form into a n-th order (global) tensor.

PDE

Partial differential equation

Basix

The FEniCS project finite element tabulator. Documentation at: https://docs.fenicsproject.org/basix/main/

Tensor

A n-dimensional array. A 0-dimensional tensor is a scalar value. A 1-dimensional tensor is a vector and a 2-dimensional tensor is a matrix. These are the most common tensors used in assemble.

DAG

A graph consisting of vertices and edges with each edge directed from one vertex to another, where following those directions will never form a closed loop. See: https://en.wikipedia.org/wiki/Directed_acyclic_graph

MPI

Message Passing Interface. A standard for passing messages in a distributed memory environment. MPI.COMM_WORLD is the most common communicator, which will use how many processors the user specify with mpirun -n M or mpiexec -n M, where M are the number of processors to distribute data over.

PETSc

PETSc, the Portable, Extensible Toolkit for Scientific Computation. See: https://petsc.org/release/ for more information.

MUMPS

MUltifrontal Massively Parallel sparse direct Solver. See: https://mumps-solver.org/index.php for more information

GMSH

Open source meshing software. See: https://gmsh.info/ for more information

OCC

The Open Cascade project. An open source 3D geometry library. See: https://dev.opencascade.org/ for more information.

PARAVIEW

Open source visualization software. See: https://www.paraview.org/ for more information

PYVISTA

Open source visualization software. See: https://pyvista.org/ for more information

DOFs

Degrees of freedom. Singular DOF

DOF

Degree of freedom. Usually the unknown coefficient of a finite element function. Plural Degrees of freedom DOFs

GJK

Gilbert–Johnson–Keerthi distance algorithm. An algorithm for determining the minimum distance between two convex hulls. For more information see: https://en.wikipedia.org/wiki/Gilbert–Johnson–Keerthi_distance_algorithm

Piola Map

A map between Eulerian and Lagrangian coordinates.