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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| Published in | ACM transactions on mathematical software Vol. 41; no. 2; pp. 1 - 40 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
01.01.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0098-3500 1557-7295 1557-7295 |
| DOI | 10.1145/2590830 |
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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 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. |
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| AbstractList | 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. |
| Author | Śmigaj, Wojciech Phillips, Joel Arridge, Simon Schweiger, Martin Betcke, Timo |
| Author_xml | – sequence: 1 givenname: Wojciech surname: Śmigaj fullname: Śmigaj, Wojciech organization: University College London and Adam Mickiewicz University in Poznań, Poland – sequence: 2 givenname: Timo surname: Betcke fullname: Betcke, Timo organization: University College London, London, UK – sequence: 3 givenname: Simon surname: Arridge fullname: Arridge, Simon organization: University College London, London, UK – sequence: 4 givenname: Joel surname: Phillips fullname: Phillips, Joel organization: University College London, London, UK – sequence: 5 givenname: Martin surname: Schweiger fullname: Schweiger, Martin organization: University College London, London, UK |
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| Cites_doi | 10.1002/nme.2579 10.1007/978-1-4757-4393-7 10.1038/35570 10.1137/S1064827503429387 10.1007/978-3-642-55483-4_3 10.1109/TAP.2008.926788 10.1103/PhysRevLett.101.084302 10.1016/S0167-739X(02)00171-1 10.1109/TAP.2013.2246854 10.1007/s00607-008-0004-9 10.1051/m2an/2010061 10.1093/qjmam/38.2.323 10.1137/120866567 10.1007/978-1-4614-4942-3 10.1002/nme.2877 10.1145/2590830 10.1007/s00607-008-0003-x 10.1007/978-0-387-68805-3 10.1002/0471764108 10.1007/978-3-540-68093-2 10.1098/rspa.1971.0097 10.1137/100812574 10.1137/0148016 10.1016/j.jcp.2005.12.001 10.1093/imanum/dri033 10.1002/nme.1620210612 10.1145/1089014.1089021 10.1038/nature06762 10.1103/RevModPhys.79.1267 10.1007/s00607-008-0002-y |
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| References | e_1_2_1_20_1 e_1_2_1_41_1 Wieleba P. (e_1_2_1_58_1) 2011; 35 Bebendorf M. (e_1_2_1_6_1) 2008 e_1_2_1_45_1 e_1_2_1_22_1 e_1_2_1_43_1 e_1_2_1_49_1 e_1_2_1_26_1 e_1_2_1_47_1 e_1_2_1_31_1 e_1_2_1_54_1 Steinbach O. (e_1_2_1_53_1) e_1_2_1_56_1 Betcke T. (e_1_2_1_8_1) 2013; 2013 e_1_2_1_12_1 Griffiths D. J. (e_1_2_1_24_1) e_1_2_1_35_1 e_1_2_1_50_1 e_1_2_1_4_1 e_1_2_1_10_1 e_1_2_1_33_1 e_1_2_1_16_1 e_1_2_1_14_1 e_1_2_1_37_1 e_1_2_1_18_1 Nédélec J.-C. (e_1_2_1_39_1) Hiptmair R. (e_1_2_1_28_1) 2012 e_1_2_1_42_1 Šolín P. (e_1_2_1_52_1) e_1_2_1_40_1 e_1_2_1_23_1 e_1_2_1_21_1 e_1_2_1_44_1 e_1_2_1_27_1 e_1_2_1_25_1 e_1_2_1_48_1 Bouwkamp C. J. (e_1_2_1_9_1) 1950; 5 e_1_2_1_29_1 Bartlett R. A. (e_1_2_1_2_1) 2007 Raviart P.-A. (e_1_2_1_46_1) e_1_2_1_7_1 e_1_2_1_30_1 e_1_2_1_55_1 e_1_2_1_5_1 e_1_2_1_57_1 e_1_2_1_3_1 e_1_2_1_13_1 e_1_2_1_34_1 e_1_2_1_51_1 e_1_2_1_1_1 e_1_2_1_11_1 e_1_2_1_32_1 e_1_2_1_17_1 e_1_2_1_38_1 e_1_2_1_15_1 e_1_2_1_36_1 e_1_2_1_19_1 |
| References_xml | – ident: e_1_2_1_21_1 doi: 10.1002/nme.2579 – volume-title: Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems ident: e_1_2_1_39_1 doi: 10.1007/978-1-4757-4393-7 – ident: e_1_2_1_26_1 – ident: e_1_2_1_18_1 doi: 10.1038/35570 – ident: e_1_2_1_25_1 doi: 10.1137/S1064827503429387 – ident: e_1_2_1_10_1 doi: 10.1007/978-3-642-55483-4_3 – ident: e_1_2_1_1_1 doi: 10.1109/TAP.2008.926788 – ident: e_1_2_1_19_1 doi: 10.1103/PhysRevLett.101.084302 – ident: e_1_2_1_5_1 doi: 10.1016/S0167-739X(02)00171-1 – ident: e_1_2_1_57_1 – volume-title: Introduction to Electrodynamics ident: e_1_2_1_24_1 – ident: e_1_2_1_44_1 doi: 10.1109/TAP.2013.2246854 – ident: e_1_2_1_42_1 – ident: e_1_2_1_50_1 – volume: 5 start-page: 321 year: 1950 ident: e_1_2_1_9_1 article-title: On Bethe's theory of diffraction by small holes publication-title: Philips Res. Rep. – ident: e_1_2_1_45_1 – ident: e_1_2_1_3_1 doi: 10.1007/s00607-008-0004-9 – ident: e_1_2_1_14_1 doi: 10.1051/m2an/2010061 – ident: e_1_2_1_34_1 doi: 10.1093/qjmam/38.2.323 – ident: e_1_2_1_48_1 – ident: e_1_2_1_56_1 – volume: 35 start-page: 173 year: 2011 ident: e_1_2_1_58_1 article-title: BEMLAB publication-title: Studies Appl. Electromagn. Mech. – ident: e_1_2_1_35_1 doi: 10.1137/120866567 – volume-title: Tech. Rep. SAND2007-5984 year: 2007 ident: e_1_2_1_2_1 – start-page: 2012 year: 2012 ident: e_1_2_1_28_1 article-title: BETL — A generic boundary element template library publication-title: Tech. Rep. – ident: e_1_2_1_32_1 – ident: e_1_2_1_7_1 – ident: e_1_2_1_15_1 doi: 10.1007/978-1-4614-4942-3 – ident: e_1_2_1_43_1 doi: 10.1002/nme.2877 – ident: e_1_2_1_38_1 – ident: e_1_2_1_51_1 doi: 10.1145/2590830 – volume: 2013 volume-title: Oberwolfach Report year: 2013 ident: e_1_2_1_8_1 – ident: e_1_2_1_4_1 doi: 10.1007/s00607-008-0003-x – volume-title: Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems year: 2008 ident: e_1_2_1_6_1 – ident: e_1_2_1_23_1 – volume-title: Numerical Approximation Methods for Elliptic Boundary Value Problems ident: e_1_2_1_53_1 doi: 10.1007/978-0-387-68805-3 – ident: e_1_2_1_37_1 – volume-title: Partial Differential Equations and the Finite Element Method ident: e_1_2_1_52_1 doi: 10.1002/0471764108 – ident: e_1_2_1_29_1 – ident: e_1_2_1_49_1 doi: 10.1007/978-3-540-68093-2 – ident: e_1_2_1_54_1 – ident: e_1_2_1_31_1 – ident: e_1_2_1_11_1 doi: 10.1098/rspa.1971.0097 – ident: e_1_2_1_13_1 doi: 10.1137/100812574 – volume-title: Mathematical Aspects of Finite Element Methods ident: e_1_2_1_46_1 – ident: e_1_2_1_33_1 doi: 10.1137/0148016 – ident: e_1_2_1_17_1 – ident: e_1_2_1_12_1 doi: 10.1016/j.jcp.2005.12.001 – ident: e_1_2_1_41_1 doi: 10.1093/imanum/dri033 – ident: e_1_2_1_22_1 – ident: e_1_2_1_16_1 doi: 10.1002/nme.1620210612 – ident: e_1_2_1_47_1 – ident: e_1_2_1_27_1 doi: 10.1145/1089014.1089021 – ident: e_1_2_1_36_1 doi: 10.1038/nature06762 – ident: e_1_2_1_20_1 doi: 10.1103/RevModPhys.79.1267 – ident: e_1_2_1_30_1 – ident: e_1_2_1_40_1 doi: 10.1007/s00607-008-0002-y – ident: e_1_2_1_55_1 |
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| Title | Solving Boundary Integral Problems with BEM |
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