Open Access

ARTICLE

Geometric Multigrid Method for Isogeometric Analysis

by Houlin Yang¹, Bingquan Zuo^1,2,*, Zhipeng Wei^1,2, Huixin Luo^1,2, Jianguo Fei^1,2

1 Key Laboratory of Metallurgical Equipment and Control Technology Ministry of Education, Wuhan University of Science and Technology, Wuhan, 430081, China
2 Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan, 430081, China

* Corresponding Author: Bingquan Zuo. Email:

Computer Modeling in Engineering & Sciences 2021, 126(3), 1033-1052. https://doi.org/10.32604/cmes.2021.014493

Received 02 October 2020; Accepted 10 December 2020; Issue published 19 February 2021

Abstract

The isogeometric analysis method (IGA) is a new type of numerical method solving partial differential equations. Compared with the traditional finite element method, IGA based on geometric spline can keep the model consistency between geometry and analysis, and provide higher precision with less freedom. However, huge stiffness matrix from the subdivision progress still leads to the solution efficiency problems. This paper presents a multigrid method based on geometric multigrid (GMG) to solve the matrix system of IGA. This method extracts the required computational data for multigrid method from the IGA process, which also can be used to improve the traditional algebraic multigrid method (AGM). Based on this, a full multigrid method (FMG) based on GMG is proposed. In order to verify the validity and reliability of these methods, this paper did some test on Poisson’s equation and Reynolds’ equation and compared the methods on different subdivision methods, different grid degrees of freedom, different cyclic structure degrees, and studied the convergence rate under different subdivision strategies. The results show that the proposed method is superior to the conventional algebraic multigrid method, and for the standard relaxed V-cycle iteration, the method still has a convergence speed independent of the grid size at the same degrees.

---

Keywords

---