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

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.