Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators

Ma, Yunyun1; Ma, Fuming2; Guo, Yukun3; Li, Jingzhi4,5,6

2023-06-01

10.4208/csiam-am.SO-2022-0009

CSIAM TRANSACTIONS ON APPLIED MATHEMATICS   Impact Factor & Quartile

2708-0560

2708-0579

This paper is devoted to the numerical computation of transmission eigen-values arising in the inverse acoustic scattering theory. This problem is first refor-mulated as a two-by-two system of boundary integral equations. Next, we develop a Schur complement operator with regularization to obtain a reduced system of bound-ary integral equations. The Nystro center dot m discretization is then used to obtain an eigenvalue problem for a matrix. In conjunction with the recursive integral method, the numerical computation of the matrix eigenvalue problem produces the indicator for finding the transmission eigenvalues. Numerical implementations are presented and archetypal examples are provided to demonstrate the effectiveness of the proposed method.

Transmission eigenvalues inverse scattering boundary integral equations Nystro?m method Schur complement spectral projection

ESCI

English

Corresponding

NSFC["11901085","11971133","11971221","GC300502-1"] ; DGUT[11771180] ; Guangdong NSF Major Fund[2021ZDZX1001] ; Shenzhen Sci-Tech Fund["RCJC20200714114556020","JCYJ20200109115422828","JCYJ20190809150413261"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Mathematics

Mathematics, Applied

WOS:000942643200004

GLOBAL SCIENCE PRESS

Web of Science

1.Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523808, Peoples R China
2.Jilin Univ, Inst Math, Changchun 130012, Peoples R China
3.Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
4.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
5.SUSTech Int Ctr Math, Shenzhen 518055, Peoples R China
6.Natl Ctr Appl Math Shenzhen, Shenzhen 518055, Peoples R China

Ma, Yunyun,Ma, Fuming,Guo, Yukun,et al. Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators[J]. CSIAM TRANSACTIONS ON APPLIED MATHEMATICS,2023,4(2).

Ma, Yunyun,Ma, Fuming,Guo, Yukun,&Li, Jingzhi.(2023).Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators.CSIAM TRANSACTIONS ON APPLIED MATHEMATICS,4(2).

Ma, Yunyun,et al."Computation of Transmission Eigenvalues by the Regularized Schur Complement for the Boundary Integral Operators".CSIAM TRANSACTIONS ON APPLIED MATHEMATICS 4.2(2023).