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Singularities in anisotropic steady‐state heat conduction using a boundary element method
Author(s) -
Mera N. S.,
Elliott L.,
Ingham D. B.,
Lesnic D.
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.407
Subject(s) - singularity , gravitational singularity , boundary element method , boundary (topology) , thermal conduction , anisotropy , mathematics , boundary value problem , mathematical analysis , computation , finite element method , geometry , convergence (economics) , boundary knot method , singular boundary method , mechanics , physics , thermodynamics , algorithm , optics , economics , economic growth
In many heat conduction problems, boundaries with sharp corners or abrupt changes in the boundary conditions give rise to singularities of various types which tend to slow down the rate of convergence with decreasing mesh size of any standard numerical method used for obtaining the solution. In this paper, it is shown how this difficulty may be overcome in the case of an anisotropic medium by a modified boundary element method. The standard boundary element method is modified to take account of the form of the singularity, without appreciably increasing the amount of computation involved. Two test examples, the first with a singularity caused by an abrupt change in a boundary condition and the second with a singularity caused by a sharp re‐entrant corner, are investigated and numerical results are presented. Copyright © 2002 John Wiley & Sons, Ltd.