Arxiv:1911.09220V2 [Cs.MS] 13 Jul 2020
MFEM: A MODULAR FINITE ELEMENT METHODS LIBRARY ROBERT ANDERSON, JULIAN ANDREJ, ANDREW BARKER, JAMIE BRAMWELL, JEAN- SYLVAIN CAMIER, JAKUB CERVENY, VESELIN DOBREV, YOHANN DUDOUIT, AARON FISHER, TZANIO KOLEV, WILL PAZNER, MARK STOWELL, VLADIMIR TOMOV Lawrence Livermore National Laboratory, Livermore, USA IDO AKKERMAN Delft University of Technology, Netherlands JOHANN DAHM IBM Research { Almaden, Almaden, USA DAVID MEDINA Occalytics, LLC, Houston, USA STEFANO ZAMPINI King Abdullah University of Science and Technology, Thuwal, Saudi Arabia Abstract. 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 dis- cretization 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 mesh- ing, 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. arXiv:1911.09220v2 [cs.MS] 13 Jul 2020 1. Introduction The Finite Element Method (FEM) is a powerful discretization technique that uses general unstructured grids to approximate the solutions of many partial differential equations (PDEs). It has been exhaustively studied, both theoretically and in practice, in the past several decades [1, 2, 3, 4, 5, 6, 7, 8]. MFEM is an open-source, lightweight, modular and scalable software library for finite elements, featuring 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 (HPC) efficiency [9].
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