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Normalization techniques for the SVE of the Green function of Helmholtz operator. (English) Zbl 1259.65181

Summary: Electromagnetic and acoustic scattering problems can be usually formulated by suitable integral equations, where the kernel is given in terms of the fundamental solution of the Helmholtz operator. We can consider a special analytic method for the singular value expansion (SVE) of this integral kernel. Note that this is an important tool for the numerical solution of scattering problems, in fact, from the knowledge of the SVE of the integral kernel, we can easily solve the corresponding integral equation. In this paper, we study the numerical approximation of the SVE of this integral kernel, where we have to consider the asymptotic behavior of the Bessel functions.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A45 Diffraction, scattering
35C15 Integral representations of solutions to PDEs

Software:

NAG; nag
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References:

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