MFEM: a modular finite element methods library. (English) Zbl 1524.65001
Summary: MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM’s goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.
MSC:
| 65-04 | Software, source code, etc. for problems pertaining to numerical analysis |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65Y05 | Parallel numerical computation |
| 65Y10 | Numerical algorithms for specific classes of architectures |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65N25 | Numerical methods for eigenvalue problems for boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
finite element methods; numerical PDEs; open-source scientific software; high-order methods; matrix-free algorithms; high-performance computingSoftware:
PCBDDC; hypre; FreeFem++; SUNDIALS; MFEM; VisIt; PETSc; Gmsh; METIS; FEniCS; OpenGL; SG; libCEED; PETSc/TS; CSparse; OCCA; GitHub; TrueGrid; STRUMPACK; GLVis; RAJA; Laghos; VTK; LIBXSMM; Axom; Isorropia; PUMI; NGSolveReferences:
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