Geometric Multigrid Method for Isogeometric Analysis  

作　　者：Houlin Yang Bingquan Zuo Zhipeng Wei Huixin Luo Jianguo Fei 

机构地区：[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

出　　处：《Computer Modeling in Engineering & Sciences》2021年第3期1033-1052,共20页工程与科学中的计算机建模（英文）

基　　金：supported by the Natural Science Foundation of Hubei Province(CN)(Grant No.2019CFB693);the Research Foundation of the Education Department of Hubei Province(CN)(Grant No.B2019003);the open Foundation of the Key Laboratory of Metallurgical Equipment and Control of Education Ministry(CN)(Grant No.2015B14).

摘　　要：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 fromthe subdivision progress still leads to the solution efficiency problems.This paper presents amultigrid method based on geometric multigrid(GMG)to solve the matrix system of IGA.This method extracts the required computational data for multigrid method fromthe 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.

关 键 词：Isogeometric method geometric multigrid method reflecting matrix subdivision strategy 

分 类 号：O24[理学—计算数学]