Journal Title
Title of Journal: Adv Comput Math
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Abbravation: Advances in Computational Mathematics
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Authors: V Domínguez M Ganesh
Publish Date: 2013/01/24
Volume: 39, Issue: 3-4, Pages: 547-584
Abstract
We propose analyze and implement interpolatory approximations and Filontype cubature for efficient and accurate evaluation of a class of wideband generalized Fourier integrals on the sphere The analysis includes derivation of i optimal order Sobolev norm error estimates for an explicit discrete Fourier transform type interpolatory approximation of spherical functions and ii a wavenumber explicit error estimate of the order mathcal Okappa ell Nr ell for ell = 0 1 2 where kappa is the wavenumber 2N2 is the number of interpolation/cubature points on the sphere and r ell depends on the smoothness of the integrand Consequently the cubature is robust for wideband from very low to very high frequencies and very efficient for highlyoscillatory integrals because the quality of the highorder approximation with respect to quadrature points is further improved as the wavenumber increases This property is a marked advantage compared to standard cubature that require at least ten points per wavelength per dimension and methods for which asymptotic convergence is known only with respect to the wavenumber subject to stable of computation of quadrature weights Numerical results in this article demonstrate the optimal order accuracy of the interpolatory approximations and the wideband cubature
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