An Iterative Method for the Inversion of the Two-Dimensional Wave Equation with a Potential
โ Scribed by Guanquan Zhang; Yu Zhang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 464 KB
- Volume
- 147
- Category
- Article
- ISSN
- 0021-9991
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โฆ Synopsis
A numerical method for a nonlinear inversion problem for the 2D wave equation with a potential is discussed. In order to avoid the ill-posedness, we substitute a coupled system of one-way wave equations for the original wave equation. An iterative algorithm is constructed to improve the accuracy of the inversion. Numerical experiments are performed on several examples to examine the effectiveness of this method.
๐ SIMILAR VOLUMES
## Abstract In this article, we apply compact finite difference approximations of orders two and four for discretizing spatial derivatives of wave equation and collocation method for the time component. The resulting method is unconditionally stable and solves the wave equation with high accuracy.
This work presents a novel boundary integral method to treat the two-dimensional potential ยฏow due to a moving body with the Lyapunov surface. The singular integral equations are derived in singularity-free form by applying the Gauss ยฏux theorem and the property of the equipotential body. The modiยฎe