Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

Roman Chapko, B. Tomas Johansson*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Original languageEnglish
Number of pages15
JournalJournal of Engineering Mathematics
VolumeEarly online
Early online date4 Apr 2016
DOIs
Publication statusE-pub ahead of print - 4 Apr 2016

Bibliographical note

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Keywords

  • boundary integral equations of the first kind
  • discrete projection method
  • exterior 3-dimensional domain
  • heat equation
  • Laguerre transformation

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