2019/01/22 by Carlos Pérez‐Arancibia, Pérez-Arancibia, Carlos, Catalin Turc +3 · 2 citations
Engineering · Physics and Astronomy · #Numerical methods in engineering #Electromagnetic Scattering and Analysis #Acoustic Wave Phenomena Research
paper · pdf · doi:10.48550/arxiv.1901.07437
This paper introduces planewave density interpolation methods for the\nregularization of weakly singular, strongly singular, hypersingular and nearly\nsingular integral kernels present in 3D Helmholtz surface layer potentials and\nassociated integral operators. Relying on Green's third identity and pointwise\ninterpolation of density functions in the form of planewaves, these methods\nallow layer potentials and integral operators to be expressed in terms of\nintegrand functions that remain smooth (at least bounded) regardless the\nlocation of the target point relative to the surface sources. Common\nchallenging integrals that arise in both Nystr "om and boundary element\ndiscretization of boundary integral equation, can then be numerically evaluated\nby standard quadrature rules that are irrespective of the kernel singularity.\nClosed-form and purely numerical planewave density interpolation procedures are\npresented in this paper, which are used in conjunction with Chebyshev-based\nNystr "om and Galerkin boundary element methods. A variety of numerical\nexamples---including problems of acoustic scattering involving multiple\ntouching and even intersecting obstacles, demonstrate the capabilities of the\nproposed technique.\n