Solving Boundary Integral Problems with BEM++
Solving Boundary Integral Problems with BEM++
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DOI：
10.1145/2590830
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
W. Smigaj;T. Betcke;S. Arridge;J. Phillips;M. Schweiger
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文献类型：
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作者：
W. Smigaj;T. Betcke;S. Arridge;J. Phillips;M. Schweiger
均匀介质中许多重要的偏微分方程问题，例如声波或电磁波的传播问题，都可以在感兴趣区域的边界上用积分方程组的形式来表示。为了解决这类问题，可以采用边界元方法。与基于区域离散化的方法(如有限元方法)相比的优点是，只需要离散化边界，这显著减少了未知数的数量。然而，边界元公式的实现要比有限元方法困难得多。在这篇文章中，我们介绍了一个新的开源的BEM++库，用于求解三维空间中的Laplace，Helmholtz和Maxwell问题的边界积分方程组。BEM++是一个C++库，具有所有重要功能的Python绑定，因此可以将该库集成到其他C++项目中，或通过Python脚本直接使用它。讨论了BEM++的内部结构和设计决策。给出了几个例子来演示该库在处理较大问题时的性能。
Many important partial differential equation problems in homogeneous media, such as those of acoustic or electromagnetic wave propagation, can be represented in the form of integral equations on the boundary of the domain of interest. In order to solve such problems, the boundary element method (BEM) can be applied. The advantage compared to domain-discretisation-based methods such as finite element methods is that only a discretisation of the boundary is necessary, which significantly reduces the number of unknowns. Yet, BEM formulations are much more difficult to implement than finite element methods. In this article, we present BEM++, a novel open-source library for the solution of boundary integral equations for Laplace, Helmholtz and Maxwell problems in three space dimensions. BEM++ is a C++ library with Python bindings for all important features, making it possible to integrate the library into other C++ projects or to use it directly via Python scripts. The internal structure and design decisions for BEM++ are discussed. Several examples are presented to demonstrate the performance of the library for larger problems.