An Iterative Meshfree Method for the Elliptic Monge-Ampere Equation in 2D

被引：3
|
作者：
Liu, Zhiyong [1 ]
He, Yinnian [1 ]
机构：
[1] Xi An Jiao Tong Univ, Ctr Computat Geosci, Sch Math & Stat, Xian 710049, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 30卷 / 05期
关键词：
Monge-Ampere equation; radial basis functions; Kansa's method; meshfree methods; convergence; DIRECT NUMERICAL-SIMULATION; OPERATOR-SPLITTING METHODS; FINITE-DIFFERENCE SOLVERS; PARTICULATE; FLOWS;
D O I：
10.1002/num.21849
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The elliptic Monge-Ampere equation is a fully nonlinear partial differential equation, which originated in geometric surface theory and has been widely applied in dynamic meteorology, elasticity, geometric optics, image processing, and others. The numerical solution of the elliptic Monge-Ampere equation has been a subject of increasing interest recently. In this article, we provide an iterative meshfree method for the elliptic Monge-Ampere equation. The nonlinear equation is simplified as series of Poisson equations with the iterative sequence. Then, the Kansa's method is used to solve these linear equations. We prove the convergence of this method. We also present some numerical experiments to demonstrate the theoretical results. (c) 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1507-1517 , 2014
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页码：1507 / 1517
页数：11
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