Efficient Computational Methods for Accurate Simulation of Wave Propagation

North Carolina State University, Raleigh NC

Investigators

Abstract

: The research project is aimed at developing accurate as well as efficient computational methods for large-scale simulations involving wave propagation in bounded and unbounded domains. The resulting methods will enable improved solution of countless engineering problems encountered in the fields of acoustics, nondestructive evaluation, earthquake engineering, medical imaging, wireless communications, oil exploration and landmine detection. Several aspects of the project are significant: In the case of modeling wave propagation in bounded domains, a new dispersion reducing technique is expected to bring down the computational cost of frequency-domain simulations by several orders of magnitude without sacrificing any accuracy. For transient (time-domain) analysis, a combination of the dispersion reducing technique and some modified time-stepping algorithms could significantly reduce the cost of analysis. The proposed investigation will also include error estimation studies to enable adaptive use of these algorithms for further reduction in computational cost. Since standard numerical methods such as finite element methods are limited to bounded domain problems, special methods are necessary to model wave propagation in unbounded domains. Proposed are two new methods - one based on space-time discretizations and the other based on continued fraction approximations. Space-time techniques are showing promise in obtaining highly accurate methods that are significantly more efficient than the existing methods of comparable accuracy. Preliminary work based on continued fraction approximations indicates the possibility of obtaining highly economical, yet accurate local absorbing boundary conditions. Other aspects of this research include devising efficient and stable schemes to couple unbounded domain methods with bounded domain methods. It is expected that the computational cost reduction from the proposed methods will enable accurate and detailed simulation of several important physical processes involving wave propagation.