Abstract
A theory of connectivity recently developed by the author is applied to construct a systematic formulation of boundary element methods. The concept of complete connectivity condition is shown to supply an alternative to boundary integral equations. The general problem of connecting solutions defined in neighbouring regions R and E is shown to lead to complete connectivity conditions which permit the formulation of three kinds of variational principles; they involve, respectively, R ∪ E, R and the common boundary between R and E, only.
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