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Volume 9, Issue 3
Fast Algorithms for Boundary Integral Equations on Elliptic Domains and Related Inverse Problems

Weifu Fang, Fu-Rong Lin & Yan-Bo Ma

DOI: 10.4208/eajam.130917.170818

East Asian J. Appl. Math., 9 (2019), pp. 485-505.

Published online: 2019-06

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  • Abstract

Fast algorithms for boundary integral equations connected with Robin boundary value problem for the Laplace equation in domains with ellipse or close to ellipse boundaries are developed. It is shown that the coefficient matrices of discretisation systems have a special structure. This fact is used to develop a fast algorithm for matrix vector multiplication and to implement it in the numerical methods used. Such an approach is especially helpful in numerical methods for inverse problems, since many methods of their solution repeatedly use forward solvers. The efficiency of the methods is illustrated by numerical examples.

  • Keywords

Robin boundary value problem, Robin inverse problem, circulant-like matrix, fast iterative methods.

  • AMS Subject Headings

65F22, 65R32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-485, author = {Weifu Fang, Fu-Rong Lin and Yan-Bo Ma}, title = {Fast Algorithms for Boundary Integral Equations on Elliptic Domains and Related Inverse Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {3}, pages = {485--505}, abstract = {

Fast algorithms for boundary integral equations connected with Robin boundary value problem for the Laplace equation in domains with ellipse or close to ellipse boundaries are developed. It is shown that the coefficient matrices of discretisation systems have a special structure. This fact is used to develop a fast algorithm for matrix vector multiplication and to implement it in the numerical methods used. Such an approach is especially helpful in numerical methods for inverse problems, since many methods of their solution repeatedly use forward solvers. The efficiency of the methods is illustrated by numerical examples.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130917.170818 }, url = {http://global-sci.org/intro/article_detail/eajam/13163.html} }
TY - JOUR T1 - Fast Algorithms for Boundary Integral Equations on Elliptic Domains and Related Inverse Problems AU - Weifu Fang, Fu-Rong Lin & Yan-Bo Ma JO - East Asian Journal on Applied Mathematics VL - 3 SP - 485 EP - 505 PY - 2019 DA - 2019/06 SN - 9 DO - http://doi.org/10.4208/eajam.130917.170818 UR - https://global-sci.org/intro/article_detail/eajam/13163.html KW - Robin boundary value problem, Robin inverse problem, circulant-like matrix, fast iterative methods. AB -

Fast algorithms for boundary integral equations connected with Robin boundary value problem for the Laplace equation in domains with ellipse or close to ellipse boundaries are developed. It is shown that the coefficient matrices of discretisation systems have a special structure. This fact is used to develop a fast algorithm for matrix vector multiplication and to implement it in the numerical methods used. Such an approach is especially helpful in numerical methods for inverse problems, since many methods of their solution repeatedly use forward solvers. The efficiency of the methods is illustrated by numerical examples.

Weifu Fang, Fu-Rong Lin and Yan-Bo Ma. (2019). Fast Algorithms for Boundary Integral Equations on Elliptic Domains and Related Inverse Problems. East Asian Journal on Applied Mathematics. 9 (3). 485-505. doi:10.4208/eajam.130917.170818
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