A numerical coordinate transformation for efficient evaluation of oscillatory integrals over wave boundary elements.

Trevelyan, J.; Honnor, M.E.

Abstract

When the Partition of Unity Method is applied to a discretised integral equation form of the Helmholtz operator, the computational cost is dominated by the evaluation of highly oscillatory integrals over discretisations. This paper presents a new numerical approach that is based on a coordinate transformation to a secondary discretisation that is aligned with an approximation to the curvilinear coordinate in which oscillation is taking place. This transforms a 2D surface integral into an equivalent set of 1D integrals that may be evaluated cheaply yet accurately. A method is proposed for dealing efficiently with difficulties that occurred at the edges of elements in previous work.

Citation

Trevelyan, J., & Honnor, M. (2009). A numerical coordinate transformation for efficient evaluation of oscillatory integrals over wave boundary elements. The Journal of integral equations and applications, 21(3), 447-468. https://doi.org/10.1216/jie-2009-21-3-447

• Journal Article Type: Article
• Publication Date: 2009
• Journal: Journal of Integral Equations and Applications
• Print ISSN: 0897-3962
• Publisher: Rocky Mountain Mathematics Consortium
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 3
• Pages: 447-468
• DOI: https://doi.org/10.1216/jie-2009-21-3-447
• Keywords: Boundary element method, waves, oscillatory integrals