Solving Eikonal equation in 2D and 3D by generalized finite difference method

被引：2

作者：

Salete, Eduardo ^{[1
]}

Flores, Jesus ^{[1
]}

Garcia, Angel ^{[1
]}

Negreanu, Mihaela ^{[2
]}

Vargas, Antonio M. ^{[2
]}

Urena, Francisco ^{[1
]}

机构：

[1] UNED, Escuela Tecn Super Ingenieros Ind, Madrid, Spain

[2] UCM, Inst Matemat Interdisciplinar, Dept Analisis Matematico Matemat Aplicada, Madrid, Spain

来源：

COMPUTATIONAL AND MATHEMATICAL METHODS | 2021年 / 3卷 / 06期

关键词：

generalized finite difference method; meshless methods; nonlinear Eikonal equation; PDEs; SYSTEM;

D O I：

10.1002/cmm4.1203

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we propose an implementation, for irregular cloud of points, of the meshless method called generalized finite difference method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulas for derivatives and solve the system of nonlinear equations using the Newton-Raphson method to obtain the approximate numerical values of the function for the discretization of the domain. It is also shown that the approximation of the scheme used is of second order. Finally, we provide several examples of its application over irregular domains in order to test accuracy of the scheme, as well as comparison with order numerical methods.

引用

页数：12

共 9 条

[1] Solving parabolic and hyperbolic equations by the generalized finite difference method [J].

Benito, J. J. ;

Urena, F. ;

Gavete, L. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 209 (02) :208-233

[2] Solving a chemotaxis-haptotaxis system in 2D using Generalized Finite Difference Method [J].

Benito, J. J. ;

Garcia, A. ;

Gavete, L. ;

Negreanu, M. ;

Urena, F. ;

Vargas, A. M. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (05) :762-777

[3] On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences [J].

Benito, J. J. ;

Garcia, A. ;

Gavete, L. ;

Negreanu, M. ;

Urena, F. ;

Vargas, A. M. .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2020, 113 :181-190

[4] Influence of several factors in the generalized finite difference method [J].

Benito, JJ ;

Ureña, F ;

Gavete, L .

APPLIED MATHEMATICAL MODELLING, 2001, 25 (12) :1039-1053

[5] Solving second order non-linear elliptic partial differential equations using generalized finite difference method [J].

Gavete, L. ;

Urena, F. ;

Benito, J. J. ;

Garcia, A. ;

Urena, M. ;

Salete, E. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 318 :378-387

[6]

Gavete ML, 2019, BIOMED J SCI TECHN R, V23, P20

[7]

Lancaster P., 1986, CURVE SURFACE FITTIN

[8] The approximation power of moving least-squares [J].

Levin, D .

MATHEMATICS OF COMPUTATION, 1998, 67 (224) :1517-1531

[9] THE FINITE-DIFFERENCE METHOD AT ARBITRARY IRREGULAR GRIDS AND ITS APPLICATION IN APPLIED MECHANICS [J].

LISZKA, T ;

ORKISZ, J .

COMPUTERS & STRUCTURES, 1980, 11 (1-2) :83-95

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