COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2003; 19:387–399 (DOI: 10.1002/cnm.598) Fast solution of problems with multiple load cases by using wavelet-compressed boundary element matrices Henrique F. Bucher 1; 2 , Luiz C. Wrobel *; 1 , Webe J. Mansur 2 and Carlos Magluta 2 1 Department of Mechanical Engineering; Brunel University; Uxbridge UB8 3PH; Middlesex; U.K. 2 Department of Civil Engineering; COPPE/Federal University of Rio de Janeiro; P.O. Box 68506; CEP 21945-910; Rio de Janeiro; Brazil SUMMARY This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called ‘virtual assem- bly’, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices—up to a small variation introduced by compression— so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique. Copyright ? 2003 John Wiley & Sons, Ltd. KEY WORDS: matrix compression; boundary element method; wavelet transforms; fast solvers 1. INTRODUCTION It is well known that the application of the boundary element method [1] for the numeri- cal solution of boundary-value problems produces non-symmetric, dense matrices, which are computationally expensive to solve using direct methods such as Gauss elimination, requiring an eort of order O(N 3 ) for systems with N degrees of freedom. To reduce the computational eort involved in the solution, several papers have been published on iterative methods such as conjugate gradients, Lanczos or GMRES [2–5]. Despite some relative success, the time necessary to achieve accurate solutions, even with well-tuned iterative solvers, is still of order O(N 2 ). Graphical plots of the boundary element method (BEM) matrices show a great deal of redun dancy, noted by large smooth surfaces, arising from an intrinsic geometry over-representation * Correspondence to: L. C. Wrobel, Department of Mechanical Engineering, Brunel University, Uxbridge, Middlesex UB8 3PH, U.K. Contract=grant sponsor: Brazilian Ministry of Education Contract=grant sponsor: Brazilian Ministry for Science and Technology Received 2 January 2001 Copyright ? 2003 John Wiley & Sons, Ltd. Accepted 17 September 2002