A comparison of domain integral evaluation techniques for boundary element methods
In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, nota...
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Published in | International journal for numerical methods in engineering Vol. 52; no. 4; pp. 417 - 432 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Chichester, UK
John Wiley & Sons, Ltd
10.10.2001
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Subjects | |
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Abstract | In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. Copyright © 2001 John Wiley & Sons, Ltd. |
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AbstractList | Abstract
In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. Copyright © 2001 John Wiley & Sons, Ltd. In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. (Author) In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically, this was seen as going against the spirit of boundary element methods, and several methods were developed to avoid this discretization, notably dual and multiple reciprocity methods and particular solution methods. These involved the representation of the interior function with a set of basis functions, generally of the radial type. In this study, meshless methods (dual reciprocity and particular solution) are compared to the direct domain integration methods. The domain integrals are evaluated using traditional methods and also with multipole acceleration. It is found that the direct integration always results in better accuracy, as well as smaller computation times. In addition, the multipole method further improves on the computation times, in particular where multiple evaluations of the integral are required, as when iterative solvers are used. The additional error produced by the multipole acceleration is negligible. Copyright © 2001 John Wiley & Sons, Ltd. |
Author | Brown, Mary J. Ingber, Marc S. Mammoli, Andrea A. |
Author_xml | – sequence: 1 givenname: Marc S. surname: Ingber fullname: Ingber, Marc S. email: ingber@me.unm.edu organization: Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A – sequence: 2 givenname: Andrea A. surname: Mammoli fullname: Mammoli, Andrea A. organization: Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A – sequence: 3 givenname: Mary J. surname: Brown fullname: Brown, Mary J. organization: Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A |
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Cites_doi | 10.1002/nme.1620260911 10.1002/(SICI)1097-0207(19990310)44:7<897::AID-NME530>3.0.CO;2-S 10.1038/324446a0 10.1002/cnm.1640090104 10.1016/0045-7825(87)90010-7 10.1016/0307-904X(92)90063-9 10.1061/(ASCE)0733-9399(1986)112:7(682) 10.1137/0907058 10.1002/cnm.1630040504 10.1002/nme.1620260912 10.1016/0955-7997(94)90010-8 10.1016/S0955-7997(97)00021-0 |
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References_xml | – volume: 65 start-page: 147 year: 1987 end-page: 164 article-title: The dual‐reciprocity boundary element formulation for non‐linear diffusion problems publication-title: Computational Methods in Applied Mechanical Engineering – volume: 112 start-page: 682 year: 1986 end-page: 695 article-title: Free vibration analysis of BEM using particular integrals publication-title: Journal of Engineering Mechanics – volume: 26 start-page: 2079 year: 1988 end-page: 2096 article-title: A new boundary element formulation for two‐ and three‐dimensional elastoplasticity using particular integrals publication-title: International Journal for Numerical Methods in Engineering – volume: 19 start-page: 17 year: 1997 end-page: 31 article-title: A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number publication-title: Engineering Analysis of Boundary Elements – volume: 2 start-page: 81 year: 1989 end-page: 93 – volume: IX start-page: 127 year: 1994 end-page: 137 – volume: XIII start-page: 325 year: 1999 end-page: 334 – start-page: 485 year: 1993 end-page: 500 – volume: 16 start-page: 124 year: 1992 end-page: 132 article-title: A boundary element approach for parabolic differential equations using a class of particular solutions publication-title: Applied Mathematical Modelling – volume: 324 start-page: 446 year: 1996 end-page: 449 article-title: A hierarchical ( log ) force‐calculation algorithm publication-title: Nature – volume: XV start-page: 517 year: 1993 end-page: 527 – volume: 7 start-page: 856 year: 1986 end-page: 869 article-title: GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems publication-title: SIAM Journal of Sciences Statistics and Computing – volume: 7 start-page: 279 issue: 4 year: 1991 end-page: 288 article-title: A boundary element approach for non‐homogeneous potential problems publication-title: Computers and Mathematics – volume: 9 start-page: 9 year: 1993 end-page: 13 article-title: A 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1994 ident: e_1_2_1_10_2 contributor: fullname: Power H – ident: e_1_2_1_12_2 doi: 10.1002/nme.1620260911 – volume: 6 start-page: 164 issue: 3 year: 1989 ident: e_1_2_1_7_2 article-title: The multiple reciprocity method: a new approach for transforming BEM domain integrals to the boundary publication-title: Engineering Analysis contributor: fullname: Nowak AJ – volume: 5 start-page: 57 year: 1994 ident: e_1_2_1_17_2 article-title: The theory of radial basis functions applied to the BEM for inhomogeneous partial differential equations publication-title: Boundary Element Communications contributor: fullname: Goldberg MA – ident: e_1_2_1_23_2 doi: 10.1002/(SICI)1097-0207(19990310)44:7<897::AID-NME530>3.0.CO;2-S – volume: 324 start-page: 446 year: 1996 ident: e_1_2_1_24_2 article-title: A hierarchical O(N log N) force‐calculation algorithm publication-title: Nature doi: 10.1038/324446a0 contributor: fullname: Barnes J – start-page: 312 volume-title: Boundary Elements year: 1982 ident: e_1_2_1_2_2 contributor: fullname: Nardini D – ident: e_1_2_1_9_2 doi: 10.1002/cnm.1640090104 – start-page: 485 volume-title: A Galerkin Implementation of the Multipole Expansion Approach for Accurate and Fast Solution of First and Second Kind Fredholm Equations year: 1993 ident: e_1_2_1_21_2 contributor: fullname: Allen EH – ident: e_1_2_1_3_2 doi: 10.1016/0045-7825(87)90010-7 – start-page: 81 volume-title: Advances in Boundary Elements year: 1989 ident: e_1_2_1_6_2 contributor: fullname: Nowak AJ – volume: 7 start-page: 279 issue: 4 year: 1991 ident: e_1_2_1_14_2 article-title: A boundary element approach for non‐homogeneous potential problems publication-title: Computers and Mathematics contributor: fullname: Zheng R – ident: e_1_2_1_15_2 doi: 10.1016/0307-904X(92)90063-9 – start-page: 41 volume-title: Boundary Element Technology year: 1994 ident: e_1_2_1_18_2 contributor: fullname: Ingber MS – volume: 23 start-page: 339 year: 1999 ident: e_1_2_1_8_2 article-title: Applications of dual MRM for determining the natural frequencies and natural modes of an Euler Bernoulli beam using the singular value decomposition method publication-title: Engineering Analysis contributor: fullname: Yeih W – volume-title: The Dual Reciprocity Boundary Element Method year: 1992 ident: e_1_2_1_5_2 contributor: fullname: Partridge PW – ident: e_1_2_1_11_2 doi: 10.1061/(ASCE)0733-9399(1986)112:7(682) – start-page: 325 volume-title: Boundary Element Technology year: 1999 ident: e_1_2_1_16_2 contributor: fullname: Partridge PW – ident: e_1_2_1_25_2 doi: 10.1137/0907058 – ident: e_1_2_1_4_2 doi: 10.1002/cnm.1630040504 – ident: e_1_2_1_13_2 doi: 10.1002/nme.1620260912 – ident: e_1_2_1_19_2 doi: 10.1016/0955-7997(94)90010-8 – start-page: 517 volume-title: Boundary Elements year: 1993 ident: e_1_2_1_20_2 contributor: fullname: Korsmeyer FT – ident: e_1_2_1_22_2 doi: 10.1016/S0955-7997(97)00021-0 |
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Snippet | In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements. Historically,... Abstract In many cases, boundary integral equations contain a domain integral. This can be evaluated by discretization of the domain into domain elements.... |
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SubjectTerms | boundary element method domain integral dual reciprocity method meshless method multipole method particular solution method |
Title | A comparison of domain integral evaluation techniques for boundary element methods |
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