On the Quadrature of Multivariate Highly Oscillatory Integrals Over Non-polytope Domains
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In this paper, we present a Levin-type method for approximating multivariate highly oscillatory integrals, subject to a non-resonance condition. Unlike existing methods, we do not require the knowledge of moments, which enables us to derive an approximation when the oscillator is complicated, and when the domain is neither a simplex nor a polytope. The accuracy of this method improves as the frequency of oscillations increases. A special case of this method has the property that the asymptotic order increases with each additional sample point.
KeywordsAsymptotic Expansion Regularity Condition Oscillatory Integral Piecewise Smooth Boundary Asymptotic Order
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