A Galerkin boundary element formulation with moving singularities

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Abstract
In conventional boundary element formulations, the singularities of the fundamental solution are usually located on the problem boundary. This leads to difficulties in evaluating solution quantities on or near the boundary. A method is presented for locating the singularities on an auxiliary boundary outside the problem domain and having this auxiliary boundary location determined automatically via a Galerkin criterion. This automatic generation of the auxiliary boundary results in a highly accurate, adaptive but non‐linear method. The number of singularities can be significantly reduced compared to conventional boundary element formulations which usually require the same number of singularities as the number of boundary elements used. The method is illustrated with three examples involving Laplace's equation in two dimensions. Excellent numerical results are obtained in all cases using only a few singularities.