A fast sweeping method for Eikonal equations
نویسندگان
چکیده
منابع مشابه
A fast sweeping method for Eikonal equations
In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve the discretized system. The crucial idea is that each sweeping ordering follows a family of characteristics...
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A uniformly second order method with a local solver based on the piecewise linear discontinuous Galerkin formulation is introduced to solve the eikonal equation with Dirichlet boundary conditions. The method utilizes an interesting phenomenon, referred as the superconvergence phenomenon, that the numerical solution of monotone upwind schemes for the eikonal equation is first order accurate on b...
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The original fast sweeping method, which is an efficient iterative method for stationary Hamilton-Jacobi equations, relies on natural ordering provided by a rectangular mesh. We propose novel ordering strategies so that the fast sweeping method can be extended efficiently and easily to any unstructured mesh. To that end we introduce multiple reference points and order all the nodes according to...
متن کاملA Fast Iterative Method for Eikonal Equations
In this paper we propose a novel computational technique to solve the Eikonal equation. The proposed method manages the list of active nodes and iteratively updates the solutions on those nodes until they converge. Nodes are added to or removed from the list based on a convergence measure, but the management of this list does not entail the the extra burden of expensive ordered data structures ...
متن کاملUniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
In [F. Li, C.-W. Shu, Y.-T. Zhang, H. Zhao, Journal of Computational Physics 227 (2008) 81918208], we developed a fast sweeping method based on a hybrid local solver which is a combination of a discontinuous Galerkin (DG) finite element solver and a first order finite difference solver for Eikonal equations. The method has second order accuracy in the L norm and a very fast convergence speed, b...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2004
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-04-01678-3