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The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy's Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED). [ABSTRACT FROM AUTHOR]

We describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of [P. Knupp, Eng. Comput., 28 (2012), pp. 419--429]. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Lagrangian--Eulerian (ALE) application [BLAST: High-order curvilinear finite elements for shock hydrodynamics. [ABSTRACT FROM AUTHOR]

We present a new approach for multi-material arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order curvilinear meshes. The method builds on and extends our previous work in the Lagrangian [V. A. Dobrev, T. V. Kolev, and R. N. Rieben, SIAM J. Sci. Comput., 34 (2012), pp. B606-B641] and remap [R. W. Anderson et al., Internat. J. Numer. Methods Fluids, 77 (2015), pp. 249-273] phases of ALE, and depends critically on a functional perspective that enables subzonal physics and material modeling [V. A. Dobrev et al., Internat. J. Numer. Methods Fluids, 82 (2016), pp. 689-706]. Curvilinear mesh relaxation is based on node movement, which is determined through the solution of an elliptic equation. The remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval. The resulting advection equation is solved by a discontinuous Galerkin (DG) formulation, combined with a customized Flux Corrected Transport (FCT) type algorithm. Because conservative fields are remapped, additional synchronization steps are introduced to preserve bounds with respect to primal fields. These steps include modification of the low-order FCT solutions, def- inition of conservative FCT uxes based on primal field bounds, and monotone transitions between primal and conservative fields. This paper describes the mathematical formulation and properties of our approach and reports a number of numerical results from its implementation in the BLAST code [BLAST: High-order finite element Lagrangian hydrocode, http://www.llnl.gov/CASC/blast]. Additional details can be found in [R. W. Anderson et al., High-Order Multi-Material ALE Hy- drodynamics (Extended Version), Tech. report LLNL-JRNL-706339, Lawrence Livermore National Laboratory, Livermore, CA, 2016]. [ABSTRACT FROM AUTHOR]

A new finite element method for solving the Euler equations in Lagrangian coordinates is proposed. The method is stabilized by adding artificial diffusion terms compatible with positivity of mass and internal energy, a minimum principle on the specific entropy, and all generalized entropy inequalities. Two options of first-order artificial diffusion are considered. One is in the spirit of the Eulerian based method (Guermond et al., 2011 [23, 22]; Zingan et al., 2013) and the other is similar to existing viscosity stabilizations in Lagrangian frame, e.g., Dobrev et al. (2012). The method is verified to be high-order for smooth solutions even with active viscosity terms. This is achieved by using high-order finite element spaces and an entropy-based viscosity stabilization that degenerates the first-order viscous terms. This stabilization automatically distinguishes smooth and singular regions. The formal accuracy and convergence properties of the proposed methods are tested on a series of benchmark problems. This is the first result extending the entropy–viscosity methodology to the Lagrangian hydrodynamics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]