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Author Jerez-Hanckes, C.; Pinto, J.
Title (up) High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs Type Journal Article
Year 2020 Publication Mathematical Modelling and Numerical Analysis Abbreviated Journal
Volume to appear Issue Pages
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Abstract We present a spectral Galerkin numerical scheme for solving Helmholtz and Laplace prob- lems with Dirichlet boundary conditions on a finite collection of open arcs in two-dimensional space. A boundary integral method is employed, giving rise to a first kind Fredholm equation whose variational form is discretized using weighted Chebyshev polynomials. Well-posedness of the discrete problems is established as well as algebraic or even exponential convergence rates depending on the regularities of both arcs and excitations. Our numerical experiments show the robustness of the method with respect to number of arcs and large wavenumber range. Moreover, we present a suitable compression algorithm that further accelerates computational times.
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ISSN 0764-583X ISBN Medium
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Call Number UAI @ eduardo.moreno @ Serial 1126
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