Application of Haar wavelets to time-domain BEM for the transient scalar wave equation

The time-domain boundary element method using the Haar wavelets is developed for reducing the computational cost of the BE wave propagation analysis. The Haar wavelets are used for the discretization of the boundary integral equation. The time variation of the unknown potential and flux is approximated using the conventional scheme. The small matrix entries of the coefficient matrix are truncated with the Beylkin-type matrix compression scheme at before and after calculation of double boundary integral. The present BEM has the numerical stability comparable to the piecewise constant Galerkin BEM. The sparsity of the coefficient matrix generated at an each time step rises as the time step proceeds; the memory requirement of the present method can be reduced in comparison with the conventional BEM. The reduction of the computational work from the conventional BE analysis is difficult because of the sparse system of the conventional time-domain BEM.