TY  - EJOU
AU  - Chang, Chih-Wen 

TI  - A Fictitious Time Integration Method for Multi-Dimensional Backward Wave Problems
T2  - Computers, Materials \& Continua

PY  - 2011
VL  - 21
IS  - 2
SN  - 1546-2226

AB  - 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 <i>u(x, y, z, t)</i> into a new one by <i>(1+τ)u(x, y, z, t)=: v(x, y, z, t, τ)</i>, such that the original wave equation is written as a new hyperbolic type partial differential equation in the space of <i>(x, y, z, t, τ)</i>. 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.
KW  - Backward wave problem
KW  -  Wave equation
KW  -  Strongly ill-posed problem
KW  -  Fictitious time integration method (FTIM)
KW  -  Group preserving scheme (GPS)

DO  - 10.3970/cmc.2011.021.087