libMesh - A C++ Finite Element Library

The `libMesh`

library is a C++ framework for the numerical simulation of partial differential equations on serial and parallel platforms. Development began in March 2002 with the intent of providing a friendly interface to a number of high-quality software packages that are currently available.

A major goal of the library is to provide support for adaptive mesh refinement (AMR) computations in parallel while allowing a research scientist to focus on the physics they are modeling. The library currently offers:

- Partitioning Algorithms
- Generic 2D Finite Elements
- 3 and 6 noded triangles (
`Tri3`

,`Tri6`

) - 4, 8, and 9 noded quadrilaterals (
`Quad4`

,`Quad8`

,`Quad9`

) - 4 and 6 noded infinite quadrilaterals (
`InfQuad4`

,`InfQuad6`

)

- 3 and 6 noded triangles (
- Generic 3D Finite Elements
- 4 and 10 noded tetrahedrals (
`Tet4`

,`Tet10`

) - 8, 20, and 27 noded hexahedrals (
`Hex8`

,`Hex20`

,`Hex27`

) - 6, 15, and 18 noded prisms (
`Prism6`

,`Prism15`

,`Prism18`

) - 5 noded pyramids (
`Pyramid5`

) - 8, 16, and 18 noded infinite hexahedrals (
`InfHex8`

,`InfHex16`

,`InfHex18`

) - 6 and 12 noded infinite prisms (
`InfPrism6`

,`InfPrism12`

)

- 4 and 10 noded tetrahedrals (
- Generic Finite Element Families
- Lagrange
- Hierarchic
- Discontinuous Monomials

- Dimension-independence
- Operators are defined to allow the same code to run unmodified on 2D and 3D applications
- The code you debug and verify on small 2D problems can immediately be applied to large, parallel 3D applications

- Sparse Linear Algebra
`PETSc`

provides a suite of iterative solvers and preconditioners for serial and parallel applications- Complex values are supported with
`PETSc`

`LASPACK`

provides iterative solvers and preconditioners for serial applications- The
`SparseMatrix`

,`NumericVector`

, and`LinearSolver`

allow for transparent switching between solver packages. Adding a new solver interface is as simple as deriving from these classes

- Mesh IO & Format Translation Utilities
- Ideas Universal (UNV) format (.unv) with support through
`MeshData`

for arbitrary float data, like boundary conditions, associated with mesh entities - Sandia National Labs ExodusII format (.exd)
- Amtec Engineering's Tecplot binary format (.plt)
- Amtec Engineering's Tecplot ascii format (.dat)
- Los Alamos National Labs GMV format (.gmv)
- AVS Unstructured UCD format (.ucd)

- Ideas Universal (UNV) format (.unv) with support through
- Mesh Creation & Modification Utilities
- refine or coarsen a mesh: prescribed, level-one-compatible, or uniform
- build equispaced n-cubes out of
`Edge2`

,`Tri3`

,`Tri6`

,`Quad4`

,`Quad8`

,`Quad9`

,`Hex8`

,`Hex20`

,`Hex27`

- build circles/spheres out of
`Tri3`

,`Tri6`

,`Quad4`

,`Quad8`

,`Quad9`

,`Hex8`

- add infinite elements to a volume-based mesh, handle symmetry planes
- convert
`Quad4`

,`Quad8`

,`Quad9`

to`Tri3`

,`Tri6`

- convert a mesh consisting of any of the fore-mentioned n-dimensional linear elements to their second-order counterparts
- distort/translate/rotate/scale a mesh
- determine bounding boxes/spheres
- extract the mesh boundary for boundary condition handling or as a separate mesh