Abstract :
The object of this paper is a wavelet-based formulation of the boundary element method (BEM) for
diffusion problems, characterized by time-dependent fundamental solution. While the BEM is a well
known and often used technique, its time-dependent formulation for diffusion problems is very rarely
used in practical applications, due to the high computational cost which characterizes it. Here, a new
formulation is proposed, which, through the use of the wavelet expansion of the time behaviour of the
boundary elements, is characterized by a lower CPU time consumption when compared with the standard
BEM diffusion formulation. The problem to be solved is transformed into an algebraic system (of higher
dimension) and its solution gives the time domain behaviour of the desired quantities; in this way, the
time stepping procedure is avoided. Together with the formulation, the analysis of the computational cost,
and two examples are given in the paper. Copyright q 2006 John Wiley & Sons, Ltd
