Application of a direct Trefftz method with domain decomposition to 2D potential problems

This article presents an application of a direct Trefftz method with domain decomposition method to the two-dimensional potential problem. In the dire ct Trefftz methods, regular T-complete functions satisfying the governing e quations are taken as the weighting functions and then, the boundary integr al equations are derived from the weighted residual expressions of the gove rning equations. Since the T-complete functions are regular, the final equa tions are also regular and therefore, much simpler than the ordinary bounda ry element methods employing the singular fundamental solutions. Their comp utational accuracy, however, is dependent on the condition number of the co efficient matrices of the algebraic system of equations. So, for improving the accuracy, we introduce the domain decomposition method to the direct Tr efftz methods. The present method is applied to the two-dimensional potenti al problem in order to confirm the validity. (C) 1999 Elsevier Science Ltd. All rights reserved.