Solving Boundary Integral Problems with BEM

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...

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Bibliographic Details
Published in:ACM transactions on mathematical software 2015-01, Vol.41 (2), p.1-40
Main Authors: Śmigaj, Wojciech, Betcke, Timo, Arridge, Simon, Phillips, Joel, Schweiger, Martin
Format: Article
Language:English
Subjects:
Boundaries
Boundary element method
Finite element method
Integral equations
Libraries
Mathematical analysis
Programming languages
Source code
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Summary: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.
ISSN:0098-3500
1557-7295
DOI:10.1145/2590830