Indirect formulations for symmetric Galerkin BEM and space derivative problems

Abstract

An indirect symmetric Galerkin BEM (SGBEM) is applied to 2D potential problems in this paper. Based on the assumption that solutions from different methods should be the same, the hypersingular matrix appeared in SGBEM is approximately expressed by those matrices appeared in asymmetric Galerkin BEM (AGBEM). As only strong and weak singularities need to be solved, the problem becomes much simpler. The space derivatives of potential are expressed with a set of new meaning distributed flux, which will produce the same potential on the boundary position for Ω in the unbounded domain Ω+Ω′, so that hypersingularity will not appear for boundary points. Therefore, there is no need of C^1,α for the spatial interpolation function (no Galerkin integration can be used for this purpose). Formulations for both the steady‐state and time‐domain potential problems are given. Three numerical examples are analyzed to demonstrate the effectiveness and accuracy of the proposed indirect method.

Citation

Yu, G.Y. (2003), "Indirect formulations for symmetric Galerkin BEM and space derivative problems", Engineering Computations, Vol. 20 No. 4, pp. 409-435. https://doi.org/10.1108/02644400310476324