### Abstract

Original language | English |
---|---|

Pages (from-to) | 217-237 |

Number of pages | 21 |

Journal | IMA Journal of Numerical Analysis |

Volume | 21 |

Issue number | 1 |

Publication status | Published - 2001 |

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### Cite this

*IMA Journal of Numerical Analysis*,

*21*(1), 217-237.

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

Research output: Contribution to journal › Article

*IMA Journal of Numerical Analysis*, vol. 21, no. 1, pp. 217-237.

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TY - JOUR

T1 - Boundary integral methods for singularly perturbed boundary value problems

AU - Langdon, S

AU - Graham, I G

N1 - ID number: ISI:000167391300009

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

M3 - Article

VL - 21

SP - 217

EP - 237

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

IS - 1

ER -