Boundary integral methods for singularly perturbed boundary value problems |
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Authors: | Langdon S; Graham I G |
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Institution: |
1 Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK, e-mail: stephen.langdon{at}durham.ac.uk e-mail: igg{at}maths.bath.ac.uk
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Abstract: | In this paper we consider boundary integral methods appliedto boundary value problems for the positive definite Helmholtz-typeproblem U + 2U = 0 in a bounded or unbounded domain,with the parameter real and possibly large. Applications arisein the implementation of spacetime boundary integralmethods for the heat equation, where is proportional to 1/(t),and t is the time step. The corresponding layer potentials arisingfrom this problem depend nonlinearly on the parameter and havekernels which become highly peaked as , causing standard discretizationschemes to fail. We propose a new collocation method with arobust convergence rate as . Numerical experiments on a modelproblem verify the theoretical results. |
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Keywords: | singular perturbation boundary integral method Helmholtz equation heat equation collocation trigonometric polynomial |
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