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High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson Extrapolation of second order finite differences

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      Abstract

      We apply second order finite difference to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Pad\'e-Richardson extrapolation to a set of finite difference eigenvalues corresponding to different grids allows to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.

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      • Record: found
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      The Deferred Approach to the Limit. Part I. Single Lattice. Part II. Interpenetrating Lattices

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        • Record: found
        • Abstract: not found
        • Article: not found

        Isospectral plane domains and surfaces via Riemannian orbifolds

         C. Gordon,  D. Webb,  S Wolpert (1992)
          Bookmark
          • Record: found
          • Abstract: not found
          • Article: not found

          Eigenvalues of the Laplacian in Two Dimensions

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            Author and article information

            Journal
            10.1016/j.jcp.2015.12.059
            1509.02795

            Mathematical & Computational physics

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