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 1D Finite Elements
- 2, 3, and 4 noded edges (
`Edge2`

,`Edge3`

,`Edge4`

).

- 2, 3, and 4 noded edges (
- 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 tetrahedra (
`Tet4`

,`Tet10`

). - 8, 20, and 27 noded hexahedra (
`Hex8`

,`Hex20`

,`Hex27`

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

,`Prism15`

,`Prism18`

). - 5, 13, and 14 noded pyramids (
`Pyramid5`

,`Pyramid13`

,`Pyramid14`

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

,`InfHex16`

,`InfHex18`

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

,`InfPrism12`

).

- 4 and 10 noded tetrahedra (
- Generic Finite Element Families
- Lagrange
- Hierarchic
- C1 elements (Hermite, Clough-Tocher)
- Discontinuous elements (Monomials, L2-Lagrange)
- Vector-valued elements (Lagrange-Vec, Nedelec first type)

- 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`

and Trilinos interfaces provide a suite of iterative solvers and preconditioners for serial and parallel applications.- Complex values are supported with
`PETSc`

. `Eigen`

(optionally 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 for reading nodal data from 2414 datasets.
- 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)
- Gmsh (http://geuz.org/gmsh) format (.msh)
- Abaqus format (.inp)
- VTK unstructured grid format (.vtk)

- 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.

- Quadrature
- Gauss-Legendre (1D and tensor product rules in 2D and 3D) tabulated up to 44th-order to high precision.
- Best available rules for triangles and tetrahedra to very high order.
- Best available monomial rules for quadrilaterals and hexahedra.

- Optimization Solvers
- Support for TAO- and nlopt-based constrained optimization solvers incorporating gradient and Hessian information.

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