Efficient implementation of power-law attenuation of elastic waves in time-domain numerical simulations

Abstract

Numerical simulation of wave propagation in the time domain is easily parallelizable on high performance computing systems due to the spatially local nature of the governing equations. The disadvantage of working in the time domain arises when lossy media must be modeled which generally gives rise to convolution-type loss terms in the governing time-domain equations. Computation of these convolutions usually requires the storage of several solution fields at thousands of previous time steps. This requirement can be memory prohibitive in three-dimensions. In this talk we present a recursive convolution approach to computing lossy (power-law) elastic wave propagation that is an extension of the one-way, one-dimensional acoustic wave equation work done by Liebler [Liebler et al., J. Acoust. Soc. Am. 116 (2004)] in order to handle multiple dimensions and shear waves. Convolutions are computed recursively by first using a nonlinear least-squares technique to fit the kernel of the convolution with a series of decaying exponentials. We demonstrate how graphical processing units (GPUs) can be used to obtain speed-up factors as high as 35 on a test computation of time-domain scattering from a highly resonant but lossy elastic cylinder. [Work sponsored by the Office of Naval Research.]