The complementary operators method applied to acoustic finite-difference time-domain simulations

Abstract

The complementary operators method (COM) has recently been introduced as a mesh-truncation technique for open-domain radiation problems in electromagnetics. The COM entails the construction of two solutions that employ absorbing boundary conditions (ABCs) with complementary behavior, i.e., the reflection coefficients associated with the two ABCs are exactly opposite each other. The average of these solutions then yields a new solution in which the errors caused by artificial reflections from the termination of grid are nearly eliminated. In this work, COM is introduced for the finite-difference time-domain (FDTD) solution of acoustics problems. The development of COM is presented in terms of Higdon’s absorbing boundary operators, but generalization to non-Higdon operators is straightforward. The effectiveness of COM in comparison to other absorbing boundary conditions is demonstrated with numerical experiments in two and three dimensions.