Improving the Performance of the Boundary Element Method with Time Dependent Fundamental Solutions by the Use of a Wavelet Expansion in the Time Domain

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.