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FESTUNG 1.0: Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2020-09-17 , DOI: 10.1016/j.camwa.2020.08.018
Balthasar Reuter , Hennes Hajduk , Andreas Rupp , Florian Frank , Vadym Aizinger , Peter Knabner

The present work documents the current state of development for our MATLAB/GNU Octave-based open source toolbox FESTUNG (Finite Element Simulation Toolbox for UNstructured Grids). The goal of this project is to design a user-friendly, research-oriented, yet computationally efficient software tool for solving partial differential equations (PDEs). Since the release of its first version, FESTUNG has been actively used for research and teaching purposes such as the design of novel algorithms and discretization schemes, benchmark studies, or just providing students with an easy-to-learn software package to study advanced numerical techniques and good programming practices. For spatial discretization, the package employs various discontinuous Galerkin (DG) methods, while different explicit, implicit, or semi-implicit Runge–Kutta schemes can be used for time stepping. The current publication discusses the most important aspects of our toolbox such as the code design concepts and various discretization procedures illustrated in some detail using a standard advection–diffusion–reaction equation. Moreover, we present selected applications already supported in FESTUNG including solvers for the two-dimensional shallow-water equations, the Cahn–Hilliard equation, and a coupled multi-physics model of free surface / subsurface flow.



中文翻译:

FESTUNG 1.0:不连续的Galerkin方法的MATLAB / GNU Octave工具箱的概述,用法和示例应用程序

本工作文件的发展为我们的MATLAB的当前状态/基于倍频GNU开源工具箱FESTUNG˚F inite ê字元素小号imulation牛逼oolbox为UN结构摆脱)。该项目的目标是设计一种用户友好的,面向研究的,但计算效率高的软件工具来求解偏微分方程(PDE)。自发布第一个版本以来,FESTUNG已被积极用于研究和教学目的,例如新颖算法和离散化方案的设计,基准研究,或者只是为学生提供易于学习的软件包来学习高级数值技术和良好的编程习惯。对于空间离散化,程序包使用各种不连续的Galerkin(DG)方法,而不同的显式,隐式或半隐式Runge-Kutta方案可用于时间步进。本出版物讨论了我们工具箱的最重要方面,例如代码设计概念和各种离散化过程,这些过程使用标准的对流-扩散-反应方程式进行了详细说明。此外,我们介绍了FESTUNG已支持的选定应用程序,包括二维浅水方程,Cahn-Hilliard方程的求解器以及自由表面/地下流动的耦合多物理场模型。

更新日期:2020-09-17
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