A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Li, Fengyan; Shu, Chi‐Wang; Zhang, Yongtao; Zhao, Hongkai

doi:10.1016/j.jcp.2008.05.018

Cited by 62 publications

(52 citation statements)

References 57 publications

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“…Most test problems presented here are taken from the literature on high order methods for hyperbolic problems : fast sweeping method [42,65], discontinuous Galerkin finite element method [7,24]. To measure the accuracy, the following error functions are defined: …”

Section: Numerical Resultsmentioning

confidence: 99%

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

Dehghan

Salehi

2010

Comput Mech

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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.

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Section: Numerical Resultsmentioning

confidence: 99%

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

Dehghan

Salehi

2010

Comput Mech

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“…In the vast literature, we cite just a few of them to illustrate the point: [27,26,19,20,23,10,16,29,25,9,17,18,7,12]. The traveltime field is mostly smooth, suggesting that high-order finite-difference methods should be effective.…”

Section: Introductionmentioning

confidence: 99%

Factored singularities and high-order Lax–Friedrichs sweeping schemes for point-source traveltimes and amplitudes

Luo

Qian

2011

Journal of Computational Physics

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“…Because of the wide stencil of high-order finite difference approximation to the derivative, some downwind informations are used, and the computational complexity of high-order finite difference type fast sweeping methods is slightly more than linear. Discontinuous Galerkin (DG) methods, which are presented in [19], can achieve high order accuracy using a compact computational stencil.…”

Section: Introductionmentioning

confidence: 99%

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Dehghan

Salehi

2009

Numerical Methods Partial

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In this work, a partial differential equation, which has several important applications, is investigated, and some techniques based on semianalytic (or quasi-numerical) approaches are developed to find its solution. In this article, the homotopy perturbation method (HPM), Adomian decomposition method, and the modified homotopy perturbation method are proposed to solve the Eikonal equation. HPM yields solution in convergent series form with easily computable terms, and in some case, yields exact solutions in one iteration. In other hand, in Adomian decomposition method, the approximate solution is considered as an infinite series usually converges to the accurate solution. Moreover, these methods do not require any discretization, linearization, or small perturbation, and therefore reduce the numerical computation a lot. Several test problems are given and results are compared with the variational iteration method.

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A second order discontinuous Galerkin fast sweeping method for Eikonal equations

Cited by 62 publications

References 57 publications

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

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

Factored singularities and high-order Lax–Friedrichs sweeping schemes for point-source traveltimes and amplitudes

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

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