An Energy Absorbing Far-Field Boundary Condition for the Elastic Wave Equation (Communications in Computational Physics, 2009)
We present an energy absorbing non-reflecting boundary condition ofClayton-Engquist type for the elastic wave equation together with a discretizationwhich is stable for any ratio of compressional to shear wave speed. We prove stabilityfor a second-order accurate finite-difference discretization of the elastic wave equationin three space dimensions together with a discretization of the proposed non-reflectingboundary condition. The stability proof is based on a discrete energy estimate and isvalid for heterogeneous materials. The proof includes all six boundaries of the computationaldomain where special discretizations are needed at the edges and corners.The stability proof holds also when a free surface boundary condition is imposed onsome sides of the computational domain.