Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 228, Issue 17, Pages 6440-6455Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.05.029
Keywords
Fast sweeping method; Eikonal equation; Factored eikonal equation; Source singularity
Funding
- NSF [DMS-0513073]
- ONR [N00014-02-1-0090]
- DARPA [N00014-02-1-0603]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [811254] Funding Source: National Science Foundation
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We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources. (C) 2009 Elsevier Inc. All rights reserved.
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