2010
DOI: 10.1007/s00466-010-0547-4
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A boundary-only meshless method for numerical solution of the Eikonal equation

Abstract: The radial basis function (RBF) collocation methods for the numerical solution of partial differential equation have been popular in recent years because of their advantage. For instance, they are inherently meshless, integration free and highly accurate. In this article we study the RBF solution of Eikonal equation using boundary knot method and analog equation method. The boundary knot method (BKM) is a meshless boundary-type radial basis function collocation technique. In contrast with the method of fundame… Show more

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Cited by 13 publications
(3 citation statements)
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“…Compared to the FEM and the BEM, this type of method is meshless, and the approximate solutions are constructed based on a cluster of scattered nodes [30][31][32][33][34][35][36]. Many meshless methods are derived from a weak-form formulation on global domain or a set of local sub-domains.…”
Section: Introductionmentioning
confidence: 99%
“…Compared to the FEM and the BEM, this type of method is meshless, and the approximate solutions are constructed based on a cluster of scattered nodes [30][31][32][33][34][35][36]. Many meshless methods are derived from a weak-form formulation on global domain or a set of local sub-domains.…”
Section: Introductionmentioning
confidence: 99%
“…for some function f . H. Zhao proposed a fast sweeping method for computing the numerical solution of the Eikonal equations on a rectangular grid [3], in [4], the authors used a boundary-only meshless method, and in [5], a differential quadrature method was employed. Moreover, a fast marching method is proposed in [6] and a fast semi-Lagrangian method in [7].…”
Section: Introductionmentioning
confidence: 99%
“…Meshless methods have been found to possess special advantages on problems to that the conventional mesh-based methods are difficult to be applied. These generally include problems with complicated boundary, moving boundary and so on [31,32,33,34,35,36,37]. A lot of meshless methods are based on a weak-form formulation on global domain or a set of local sub-domains.…”
Section: Introductionmentioning
confidence: 99%