Singular boundary method for 3D time-harmonic electromagnetic scattering problems. (English) Zbl 1481.78005
Summary: A frequency domain singular boundary method is presented for solving 3D time-harmonic electromagnetic scattering problem from perfect electric conductors. To avoid solving the coupled partial differential equations with fundamental solutions involving hypersingular terms, we decompose the governing equation into a system of independent Helmholtz equations with mutually coupled boundary conditions. Then the singular boundary method employs the fundamental solutions of the Helmholtz equations to approximate the scattered electric field variables. To desingularize the source singularity in the fundamental solutions, the origin intensity factors are introduced. In the novel formulation, only the origin intensity factors for fundamental solutions of 3D Helmholtz equations and its derivatives need to be considered which have been derived in the paper. Several numerical examples involving various perfectly conducting obstacles are carried out to demonstrate the validity and accuracy of the present method.
MSC:
| 78A45 | Diffraction, scattering |
| 78M15 | Boundary element methods applied to problems in optics and electromagnetic theory |
| 35P25 | Scattering theory for PDEs |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 65N80 | Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
Keywords:
singular boundary method; origin intensity factor; method of fundamental solutions; electromagnetic scattering; boundary-type methodReferences:
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