Boundary integral methods for singularly perturbed boundary value problems

S Langdon, I G Graham

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.
Original languageEnglish
Pages (from-to)217-237
Number of pages21
JournalIMA Journal of Numerical Analysis
Volume21
Issue number1
Publication statusPublished - 2001

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Boundary Integral Method
Singularly Perturbed Boundary Value Problem
Boundary value problems
Infinity
Layer Potentials
Discretization Scheme
Experiments
Hermann Von Helmholtz
Unbounded Domain
Collocation Method
Heat Equation
Positive definite
Convergence Rate
Bounded Domain
Space-time
Directly proportional
Boundary Value Problem
Numerical Experiment
Roots
kernel

Cite this

Boundary integral methods for singularly perturbed boundary value problems. / Langdon, S; Graham, I G.

In: IMA Journal of Numerical Analysis, Vol. 21, No. 1, 2001, p. 217-237.

Research output: Contribution to journalArticle

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