Research

Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in R-3


Reference:

Graham, I. G. and Sloan, I. H., 2002. Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in R-3. Numerische Mathematik, 92 (2), pp. 289-323.

Related documents:

This repository does not currently have the full-text of this item.
You may be able to access a copy if URLs are provided below.

Abstract

In this paper we describe and analyse a class of spectral methods, based on spherical polynomial approximation, for second-kind weakly singular boundary integral equations arising from the Helmholtz equation on smooth closed 3D surfaces diffeomorphic to the sphere. Our methods are fully discrete Galerkin methods, based on the application of special quadrature rules for computing the outer and inner integrals arising in the Galerkin matrix entries. For the outer integrals we use, for example, product-Gauss rules. For the inner integrals, a variant of the classical product integration procedure is employed to remove the singularity arising in the kernel. The key to the analysis is a recent result of Sloan and Womersley on the norm of discrete orthogonal projection operators on the sphere. We prove that our methods are stable for continuous data and superalgebraically convergent for smooth data. Our theory includes as a special case a method closely related to one of those proposed by Wienert (1990) for the fast computation of direct and inverse acoustic scattering in 3D.

Details

Item Type Articles
CreatorsGraham, I. G.and Sloan, I. H.
DOI10.1007/s002110100343
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7405
Additional InformationID number: ISI:000178009600004

Export

Actions (login required)

View Item