Numerische Mathematik

, Volume 103, Issue 4, pp 643–665 | Cite as

On the Quadrature of Multivariate Highly Oscillatory Integrals Over Non-polytope Domains

  • Sheehan OlverEmail author


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.


Asymptotic Expansion Regularity Condition Oscillatory Integral Piecewise Smooth Boundary Asymptotic Order 
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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical PhysicsCentre for Mathematical SciencesCambridgeUK

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