Sparse convolution quadrature for time domain boundary integral formulations of the wave equation
Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem, we employ the convolution quadrature method for the discretization in time and the Galerkin bou...
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| Veröffentlicht in: | IMA journal of numerical analysis 2009-01, Vol.29 (1), p.158-179 |
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| creator | Hackbusch, W. Kress, W. Sauter, S. A. |
| description | Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem, we employ the convolution quadrature method for the discretization in time and the Galerkin boundary element method for the space discretization. We introduce a simple a priori cut-off strategy where small entries of the system matrices are replaced by zero. The threshold for the cut-off is determined by an a priori analysis which will be developed in this paper. This analysis will also allow to estimate the effect of additional perturbations such as panel clustering and numerical integration on the overall discretization error. This method reduces the storage complexity for time domain integral equations from O(M2N) to O(M2N½ logM), where N denotes the number of time steps and M is the dimension of the boundary element space. |
| doi_str_mv | 10.1093/imanum/drm044 |
| format | Article |
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This method reduces the storage complexity for time domain integral equations from O(M2N) to O(M2N½ logM), where N denotes the number of time steps and M is the dimension of the boundary element space.</description><identifier>ISSN: 0272-4979</identifier><identifier>EISSN: 1464-3642</identifier><identifier>DOI: 10.1093/imanum/drm044</identifier><identifier>CODEN: IJNADH</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Approximations and expansions ; boundary element method ; convolution quadrature ; Exact sciences and technology ; Integral equations ; Mathematical analysis ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical approximation ; Partial differential equations ; retarded potentials ; Sciences and techniques of general use ; sparse representation</subject><ispartof>IMA journal of numerical analysis, 2009-01, Vol.29 (1), p.158-179</ispartof><rights>The author 2008. 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A.</creatorcontrib><title>Sparse convolution quadrature for time domain boundary integral formulations of the wave equation</title><title>IMA journal of numerical analysis</title><description>Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem, we employ the convolution quadrature method for the discretization in time and the Galerkin boundary element method for the space discretization. We introduce a simple a priori cut-off strategy where small entries of the system matrices are replaced by zero. The threshold for the cut-off is determined by an a priori analysis which will be developed in this paper. This analysis will also allow to estimate the effect of additional perturbations such as panel clustering and numerical integration on the overall discretization error. This method reduces the storage complexity for time domain integral equations from O(M2N) to O(M2N½ logM), where N denotes the number of time steps and M is the dimension of the boundary element space.</description><subject>Approximations and expansions</subject><subject>boundary element method</subject><subject>convolution quadrature</subject><subject>Exact sciences and technology</subject><subject>Integral equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical approximation</subject><subject>Partial differential equations</subject><subject>retarded potentials</subject><subject>Sciences and techniques of general use</subject><subject>sparse representation</subject><issn>0272-4979</issn><issn>1464-3642</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqFkE1r3DAQhkVpoNukx9xFIZCLm7GkyNIxLPliQ3PIByUXMZal1qltbSQryf77evGSa08Dw_M-M7yEHJbwowTNT9oeh9yfNLEHIT6RRSmkKLgU7DNZAKtYIXSlv5CvKT0DgJAVLAjerTEmR20YXkOXxzYM9CVjE3HM0VEfIh3b3tEm9NgOtA55aDBuaDuM7nfEbkv0ucNtMNHg6fjH0Td8ddRNmu32gOx57JL7tpv75OHi_H55VdzcXl4vz24KKyoYC64qqaFEz61wzDZKK1Wi1KcN1oI5piXWNdfO1hK98rLm6EApra0Cjw3wffJ99q5jeMkujeY55DhMJw0rOSgBSk5QMUM2hpSi82Ydp9rixpRgtiWauUQzlzjxRzspJoudjzjYNn2EWCm10sAn7njmQl7_V7l7oU2je_-AMf41suLVqbn69WQYW_28k49Ls-L_AKLKk7Y</recordid><startdate>20090101</startdate><enddate>20090101</enddate><creator>Hackbusch, W.</creator><creator>Kress, W.</creator><creator>Sauter, S. 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Scientific computation</topic><topic>Numerical approximation</topic><topic>Partial differential equations</topic><topic>retarded potentials</topic><topic>Sciences and techniques of general use</topic><topic>sparse representation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hackbusch, W.</creatorcontrib><creatorcontrib>Kress, W.</creatorcontrib><creatorcontrib>Sauter, S. 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| ispartof | IMA journal of numerical analysis, 2009-01, Vol.29 (1), p.158-179 |
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| language | eng |
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| source | Oxford University Press Journals All Titles (1996-Current) |
| subjects | Approximations and expansions boundary element method convolution quadrature Exact sciences and technology Integral equations Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Partial differential equations retarded potentials Sciences and techniques of general use sparse representation |
| title | Sparse convolution quadrature for time domain boundary integral formulations of the wave equation |
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