Fast sweeping method
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In applied mathematics, the fast sweeping method is a numerical method for solving boundary value problems of the Eikonal equation.
where is an open set in and is a function with positive values and is a well-behaved boundary of the open set and is the norm.
Introduction
Fast sweeping method is an iterative method which uses upwind difference for discretization and uses Gauss–Seidel iterations with alternating sweeping ordering to solve the discretized Eikonal equation on a rectangular grid. The origins of this approach lie in control theory. Although fast sweeping methods have existed in control theory, it was first proposed for Eikonal equations[1] by Hongkai Zhao, an applied mathematician at the University of California, Irvine.
References
- ^ Zhao, Hongkai (2005-01-01). "A fast sweeping method for Eikonal equations". Mathematics of Computation. 74 (250): 603–627. doi:10.1090/S0025-5718-04-01678-3. ISSN 0025-5718.
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