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Solving Boundary Integral Problems with BEM++

Smigaj, W; Arridge, S; Betcke, T; Phillips, J; Schweiger, M; (2015) Solving Boundary Integral Problems with BEM++. ACM Transactions on Mathematical Software , 41 (2) , Article 6. 10.1145/2590830. Green open access

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Abstract

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 paper we present BEM++, a novel open-source library for the solution of boundary integral equation for Laplace and Helmholtz 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.

Type: Article
Title: Solving Boundary Integral Problems with BEM++
Open access status: An open access version is available from UCL Discovery
DOI: 10.1145/2590830
Publisher version: http://dx.doi.org/10.1145/2590830
Language: English
Additional information: Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author. 2015 Copyright is held by the author/owner(s).
Keywords: boundary element methods, boundary integral equations, C++, Python Interface
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1380119
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