Open Access

ARTICLE

A Fictitious Time Integration Method for Multi-Dimensional Backward Wave Problems

Chih-Wen Chang¹

1 Grid Applied Technology Division, National Center for High-Performance Computing, Taichung40763, Taiwan. Tel: +886-4-24620202 ext.860. E-mail: 0903040@nchc.narl.org.tw

Computers, Materials & Continua 2011, 21(2), 87-106. https://doi.org/10.3970/cmc.2011.021.087

Abstract

We address a new numerical approach to deal with these multi-dimensional backward wave problems (BWPs) in this study. A fictitious time τ is utilized to transform the dependent variable u(x, y, z, t) into a new one by (1+τ)u(x, y, z, t)=: v(x, y, z, t, τ), such that the original wave equation is written as a new hyperbolic type partial differential equation in the space of (x, y, z, t, τ). Besides, a fictitious viscous damping coefficient can be employed to strengthen the stability of numerical integration of the discretized equations by using a group preserving scheme. Several numerical instances demonstrate that the present scheme can be utilized to retrieve the initial wave very well. Even though the noisy final data are very large, the fictitious time integration method is also robust against disturbance.

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Keywords

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