Summer 2021 A fast multiscale Galerkin method for solving a boundary integral equation in a domain with corners
Xiangling Chen, Ying Jiang
J. Integral Equations Applications 33(2): 193-228 (Summer 2021). DOI: 10.1216/jie.2021.33.193


A fast multiscale Galerkin method is proposed for solving the boundary integral equation derived from the Dirichlet problem of the Laplace equation in a domain with corners. It is well known that the integral operator in the equation can be split into two operators, one is noncompact, the other is compact. We design two truncation strategies for the representation matrices of these operators, respectively, which compress these two dense matrices to sparse ones having only 𝒪(2n) number of nonzero entries, where 2n is the number of the wavelet basis functions used in the method. We prove that the proposed truncation strategies do not ruin the stability and convergence rate of the integral equation. Numerical experiments are presented to verify the theoretical results and demonstrate the effectiveness of the method.


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Xiangling Chen. Ying Jiang. "A fast multiscale Galerkin method for solving a boundary integral equation in a domain with corners." J. Integral Equations Applications 33 (2) 193 - 228, Summer 2021.


Received: 21 June 2020; Revised: 6 October 2020; Accepted: 14 October 2020; Published: Summer 2021
First available in Project Euclid: 31 August 2021

MathSciNet: MR4306870
zbMATH: 1481.65243
Digital Object Identifier: 10.1216/jie.2021.33.193

Primary: 45L05 , 65M38 , 65R20

Keywords: boundary integral equation , domains with corners , fast Galerkin methods

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium


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Vol.33 • No. 2 • Summer 2021
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