The solution algorithm to the absorptive acoustic scalar wave equation with spatially varying velocity and absorptive fields is numerically examined in the context of the k-space time-domain scattering formalism to construct an absorbing boundary potential which eliminates wraparound and edge effects. The absorptive potential is constructed by using the absorptive coefficient, i.e., the coefficient of the first temporal derivative in the differential equation. Numerical solutions, in two dimensions, show the stability of the algorithm and the elimination of wraparound and edge reflections through use of the constructed absorptive potential. The numbers of calculations and storage requirements per time step are on the order of N log 2 N and N, respectively, where N is the number of points into which the problem is discretized.

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