Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4967179 | Journal of Computational Physics | 2017 | 24 Pages |
Abstract
A true meshless integration-free method based on Taylor series named Taylor Meshless Method (TMM) has been proposed recently to solve Partial Differential Equations (PDEs), where the shape functions are high degree polynomials and the discretization concerns only the boundary. With high computational efficiency and exponential convergence, the TMM has been confirmed to be very robust in linear problems, including large-scale cases. In this paper, the TMM and the Automatic Differentiation (AD) are combined with the Newton method to solve non-linear elliptic PDEs, where the AD is used to compute shape functions in a fast manner. The numerical results illustrate that the proposed algorithm is very accurate and efficient in solving non-linear elliptic problems.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jie Yang, Heng Hu, Yao Koutsawa, Michel Potier-Ferry,