NDLI: A boundary-only meshless method for numerical solution of the Eikonal equation

Content Provider	Springer Nature Link
Author	Dehghan, Mehdi Salehi, Rezvan
Copyright Year	2010
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 fundamental solution (MFS), the BKM uses the non-singular general solution instead of the singular fundamental solution to obtain the homogeneous solution. Similar to MFS, the RBF is employed to approximate the particular solution via the dual reciprocity principle. In the current paper, we applied the idea of analog equation method (AEM). According to AEM, the nonlinear governing operator is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. Finally numerical results and discussions are presented to show the validity and efficiency of the proposed method.
Starting Page	283
Ending Page	294
Page Count	12
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	47
Issue Number	3
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-11-04
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Boundary-type meshless methods Boundary knot method Analog equation method Radial basis function Hamilton–Jacobi equations Eikonal equation Classical Continuum Physics Computational Science and Engineering Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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