A relation between the logarithmic capacity and the condition number of the BEM-matrices

W. Dijkstra, R.M.M. Mattheij

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)

Abstract

We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions.
Original languageEnglish
Pages (from-to)665-680
JournalCommunications in Numerical Methods in Engineering
Volume23
Issue number7
DOIs
Publication statusPublished - 2007

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