Numerical evaluation of two-dimensional partition of unity boundary integrals for Helmholtz problems.

Honnor, M.E.; Trevelyan, J.; Huybrechs, D.

Abstract

There has been considerable attention given in recent years to the problem of extending finite and boundary element-based analysis of Helmholtz problems to higher frequencies. One approach is the Partition of Unity Method, which has been applied successfully to boundary integral solutions of Helmholtz problems, providing significant accuracy benefits while simultaneously reducing the required number of degrees of freedom for a given accuracy. These benefits accrue at the cost of the requirement to perform some numerically intensive calculations in order to evaluate boundary integrals of highly oscillatory functions. In this paper we adapt the numerical steepest descent method to evaluate these integrals for two-dimensional problems. The approach is successful in reducing the computational effort for most integrals encountered. The paper includes some numerical features that are important for successful practical implementation of the algorithm.

Citation

Honnor, M., Trevelyan, J., & Huybrechs, D. (2010). Numerical evaluation of two-dimensional partition of unity boundary integrals for Helmholtz problems. Journal of Computational and Applied Mathematics, 234(6), 1656-1662. https://doi.org/10.1016/j.cam.2009.08.012

• Journal Article Type: Article
• Publication Date: 2010
• Deposit Date: May 5, 2010
• Journal: Journal of Computational and Applied Mathematics
• Print ISSN: 0377-0427
• Electronic ISSN: 1879-1778
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 234
• Issue: 6
• Pages: 1656-1662
• DOI: https://doi.org/10.1016/j.cam.2009.08.012
• Keywords: Partition of unity, Boundary integrals, Helmholtz, Oscillatory integrals, Numerical steepest descent
• Public URL: https://durham-repository.worktribe.com/output/1552939