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A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0

Área de investigaciónMatemáticas, Física e Ingeniería
TítuloA tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0
Tipo de publicaciónArtículo de revista
Año de publicación2020
AutoresBadia, S., y A. F. Martin
Type of ArticleArticle
KeywordsFinite elements, Object-Oriented Programming, Partial Differential Equations}, {Mathematical software

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory platforms. It provides a rich set of tools for numerical discretization and built-in scalable solvers for the resulting linear systems of equations. An application expert that wants to simulate a PDE-governed problem has to extend the framework with a description of the weak form of the PDE at hand (and additional perturbation terms for non-conforming approximations). We show how to use the library by going through three different tutorials. The first tutorial simulates a linear PDE (Poisson equation) in a serial environment for a structured mesh using both continuous and discontinuous Galerkin finite element methods. The second tutorial extends it with adaptive mesh refinement on octree meshes. The third tutorial is a distributed-memory version of the previous one that combines a scalable octree handler and a scalable domain decomposition solver. The exposition is restricted to linear PDEs and simple geometries to keep it concise. The interested user can dive into more tutorials available in the FEMPAR public repository to learn about further capabilities of the library, e.g., nonlinear PDEs and nonlinear solvers, time integration, multi-field PDEs, block preconditioning, or unstructured mesh handling. Program summary Program Title: FEMPAR Program Files doi: http://dx.doi.org/10.17632/dtx487wp57.1 Licensing provisions: GNU General Public License 3 Programming language: MPI, Fortran2003/2008 (Object-Oriented Programming features) Nature of problem: Computational simulation of a broad range of large-scale application problems governed by Partial Differential Equations Solution method: Arbitrary-order grad-, curl-, and div-conforming finite elements on n-cube and n-simplex meshes. Continuous and Discontinuous Galerkin FEM. Adaptive Mesh Refinement and Coarsening via forests-of-octrees. Diagonally Implicit Runge-Kutta time integrators. Newton-Raphson linearization. Block preconditioning for multiphysics applications. Multilevel Balancing Domain Decomposition by Constraints preconditioning. Krylov subspace iterative solvers. Sparse direct solvers. Additional comments: Program Github repository https://github.com/fempar/fempar Program website http://www.fempar.org (C) 2019 Elsevier B.V.