并行有限元库FEMPAR v1 .0.0的教程驱动介绍
A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0
摘要：
这项工作是FEMPAR科学软件库的用户指南。FEMPAR是一个开源的面向对象的框架，用于在分布式内存平台上使用有限元法模拟偏微分方程（PDE）。它为数值离散化提供了一套丰富的工具，并为所得线性方程组提供了内置的可扩展求解器。想要模拟偏微分方程控制问题的应用专家必须扩展框架，描述手头的偏微分方程的弱形式（以及用于非一致近似的附加扰动项）。我们通过三个不同的教程展示如何使用该库。第一个教程模拟一个线性PDE（泊松方程）在一个连续的环境中的结构网格使用连续和不连续的伽辽金有限元法。第二个教程扩展了它与自适应网格细化八叉树网格。第三个教程是前一个教程的分布式内存版本，它结合了一个可伸缩的八叉树处理程序和一个可伸缩的域分解求解器。论述仅限于线性偏微分方程和简单的几何形状，以保持简洁。感兴趣的用户可以深入了解FEMPAR公共存储库中的更多教程，以了解该库的更多功能，例如，非线性偏微分方程和非线性求解器，时间积分，多场偏微分方程，块预处理，或非结构化网格处理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
