# 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.