Indirect formulations for symmetric Galerkin BEM and space derivartive problems
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 Omega in the unbounded domain Omega+Omega', so that hypersingularity will not appear for boundary points. Therefore, there is no need of C-1,C-alpha 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.
boundary element method galerkin technique steady state time domain