On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-03-19
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
This paper considers some multiscale radial basis function collocation methods for solving the two-dimensional Monge–Ampère equation with Dirichlet boundary.
We discuss and study the performance of the three kinds of multiscale methods.
The first method is the cascadic meshfree method, which was proposed by Liu and He (2013).
The second method is the stationary multilevel method, which was proposed by Floater and Iske (1996), and is used to solve the fully nonlinear partial differential equation in the paper for the first time.
The third is the hierarchical radial basis function method, which is constructed by employing successive refinement scattered data sets and scaled compactly supported radial basis functions with varying support radii.
Compared with the first two methods, the hierarchical radial basis function method can not only solve the present problem on a single level with higher accuracy and lower computational cost but also produce highly sparse nonlinear discrete system.
These observations are obtained by taking the direct approach of numerical experimentation.
American Psychological Association (APA)
Liu, Zhiyong& Xu, Qiuyan. 2020. On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1193472
Modern Language Association (MLA)
Liu, Zhiyong& Xu, Qiuyan. On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation. Mathematical Problems in Engineering No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1193472
American Medical Association (AMA)
Liu, Zhiyong& Xu, Qiuyan. On Multiscale RBF Collocation Methods for Solving the Monge–Ampère Equation. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1193472
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193472