Toeplitz-type approximations to the Hadamard integral operator and their applications to electromagnetic cavity problems

Authors:
Jiming Wu;Yingxi Wang;Wen Li;Weiwei Sun
Affiliations:
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, PR China;Department of Mathematics, City University of Hong Kong, Hong Kong, PR China;Department of Mathematics, South China Normal University, Guangzhou, 510631, PR China;Department of Mathematics, City University of Hong Kong, Hong Kong, PR China
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

In this paper, we present five Toeplitz-type schemes for the Hadamard finite-part integral operator. These discrete schemes are of Toeplitz or nearly Toeplitz structure, which gives many advantages in developing fast linear solvers for numerical solution of intego-differential equations. Two examples are presented to confirm our theoretical analysis of approximations to the Hadamard finite-part integrals and to show the accuracy of schemes for solving integral equations with a hypersingular kernel. Finally, we apply our algorithms for electromagnetic scattering from cavities. Numerical results show that these algorithms are efficient.