EFFICIENT ANALYTICAL INTEGRATION OF SYMMETRICAL GALERKIN BOUNDARY INTEGRALS OVER CURVED ELEMENTS - THERMAL CONDUCTION FORMULATION

Substantial improvements are reported in the computational efficiency of Galerkin boundary element analysis (BEA) employing curved continuou s boundary elements. A direct analytical treatment of the singular dou ble integrations involved in Galerkin BEA, adapting a limit to the bou ndary concept used successfully in collocation BEA, is used to obviate significant computation in the determination of the Galerkin coeffici ent matrices. Symbolic manipulation has been strategically employed to aid in the analytical evaluation of the singular contributions to the se double integrals. The analytical regularization procedure separates the potentially singular Galerkin integrands into an essentially sing ular but simple part, plus a regular remainder that can be integrated numerically. The finite contribution from the simplified singular term is then computed analytically. It is shown that the key to containing the explosive growth in the length of the formulae associated with su ch a hybrid analytical/numerical integration scheme is the strategic t iming of when to take the limit to the boundary. This regularization a lso isolates the contribution from the curvature of the boundary eleme nt, thus facilitating enhanced computational efficiency in problems wi th many straight elements. Example problems are presented to quantify the performance of this approach. It is concluded that with these tech niques, Galerkin symmetric BEA can be more efficient than its collocat ion-based counterpart.