Time-domain lifted wavelet collocation method for modeling nonlinear wave propagation

Abstract

A time-domain adaptive numerical method for modeling nonlinear wave propagation is developed. This method is based on a second-generation wavelet collocation using a lifting scheme and makes use of the multilevel decomposition nature of the scheme to allow for automatic grid refinement according to the magnitude of waveform steepening. The multiplication in the nonlinear term is also easy due to the collocation nature. With thresholding, the solution is compact at every level of resolution and computed only at collocation points associated with the remaining significant wavelet coefficients. The error tolerance and compression ratio of the new method are totally controlled by the threshold value used. This brings substantial savings in computation time when compared to the conventional finite difference scheme on a uniformly fine grid.