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HILBERT - a MATLAB implementation of adaptive 2D-BEM

HILBERT 适应 2D-BEM 的 MATLAB 实现

作     者:Aurada, Markus Ebner, Michael Feischl, Michael Ferraz-Leite, Samuel Fuehrer, Thomas Goldenits, Petra Karkulik, Michael Mayr, Markus Praetorius, Dirk 

作者机构:Vienna Univ Technol A-1040 Vienna Austria Pontificia Univ Catolica Chile Santiago Chile Max Planck Inst Math Sci D-04103 Leipzig Germany 

出 版 物:《NUMERICAL ALGORITHMS》 (数值算法)

年 卷 期:2014年第67卷第1期

页      面:1-32页

核心收录:

学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基  金:TU graduate school Partial Differential Equations in Technical Systems - Modelling, Simulation, and Control - Vienna University of Technology Innovative Projects Initiative by Vienna University of Technology FWF project Adaptive Boundary Element Method Austrian Science Fund (FWF) [P21732] CONICYT Austrian Science Fund (FWF) [P21732] Funding Source: Austrian Science Fund (FWF) 

主  题:Boundary element methods Adaptive mesh-refinement A posteriori error estimation MATLAB implementation 

摘      要:We report on the Matlab program package HILBERT. It provides an easily-accessible implementation of lowest order adaptive Galerkin boundary element methods for the numerical solution of the Poisson equation in 2D. The library was designed to serve several purposes: The stable implementation of the integral operators may be used in research code. The framework of Matlab ensures usability in lectures on boundary element methods or scientific computing. Finally, we emphasize the use of adaptivity as general concept and for boundary element methods in particular. In this work, we summarize recent analytical results on adaptivity in the context of BEM and illustrate the use of HILBERT. Various benchmarks are performed to empirically analyze the performance of the proposed adaptive algorithms and to compare adaptive and uniform mesh-refinements. In particular, we do not only focus on mathematical convergence behavior but also on the usage of critical system resources such as memory consumption and computational time. In any case, the superiority of the proposed adaptive approach is empirically supported.

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