Dispersion analysis in wave propagation using parametrized mimetic finite differences

Abstract

Wave propagation simulations using numerical methods are subject to dispersion errors due to the discrete nature of the differentiation operator. To minimize the effects of dispersion, high-order operators are preferred to solve the wave propagation model. The mimetic finite-difference method is a family of fourth-order finite-difference operators which can be constructed by varying a set of six free parameters. In this work, I explore the effect of varying these parameters on the dispersion of elastic waves, in search of the optimal set of values to minimize this anomaly in a one-dimensional problem.