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

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.本工作为FEMPAR科学软件库的用户指南。FEMPAR是一款开源面向对象框架，可在分布式内存平台上借助有限元法对偏微分方程（Partial Differential Equations，以下简称PDEs）开展数值模拟，其提供了丰富的数值离散化工具集，并为求解所得的线性方程组内置了可扩展求解器。若应用领域专家希望对受PDE支配的问题开展数值模拟，需基于当前PDE的弱形式描述（以及针对非协调近似的额外扰动项）对该框架进行扩展。本文通过三个不同的教程示例演示该库的使用方法：第一个教程在串行环境下针对结构化网格，采用连续与间断伽辽金有限元法，对线性PDE（泊松方程，Poisson equation）开展数值模拟；第二个教程在此基础上扩展了八叉树网格上的自适应网格细化功能；第三个教程则为前一教程的分布式内存版本，结合了可扩展八叉树处理模块与可扩展区域分解求解器。为保持行文简洁，本文阐述内容仅限线性PDE与简单几何构型，有进一步学习需求的用户可前往FEMPAR公开代码仓库，查阅更多教程以了解该库的更多功能，例如非线性PDE与非线性求解器、时间积分、多场PDE、块预条件或非结构化网格处理等。