A posteriori evaluation of wave reflection for adaptive analysis of wave propagation in unbounded domains

Abstract

An adaptive analysis procedure is proposed as a new paradigm with enhanced efficiency and reliability for numerical analysis of wave propagation in unbounded domains. In the context of one-dimensional wave propagation, a local solution procedure is designed based on the method of characteristics for a posteriori evaluation of reflected waves. It is shown that the strain associated with the reflected wave exhibit excellent correlation with the order of the absorbing boundary condition employed, and thus can effectively be used as an error estimator. A simple adaptive analysis algorithm is designed to demonstrate the use of the error estimator in adaptively adjusting the order of the absorbing boundary condition to control, within predetermined tolerance, spurious wave reflection from the boundary of truncation. This leads to the use of an optimal-order absorbing boundary condition that results in solutions of desired accuracy.