In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“t...In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“tensorproduct”and“iso-parametric”feature,all the Gaussian integral points in particular element can be mapped to a global matrix using a transformation matrix that varies from element.Then the derivatives of Gauss integral points are computed in parallel,the results of which can be stored in a global matrix.And a middle layer is constructed to assemble the final stiffness matrices in parallel.The numerical example results show that:the method presented in the paper can reduce calculation time and improve the use rate of computing resources.展开更多
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 consis...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.展开更多
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).
文摘In this paper,a new computation scheme based on parallelization is proposed for Isogeometric analysis.The parallel computing is introduced to the whole progress of Isogeometric analysis.Firstly,with the help of the“tensorproduct”and“iso-parametric”feature,all the Gaussian integral points in particular element can be mapped to a global matrix using a transformation matrix that varies from element.Then the derivatives of Gauss integral points are computed in parallel,the results of which can be stored in a global matrix.And a middle layer is constructed to assemble the final stiffness matrices in parallel.The numerical example results show that:the method presented in the paper can reduce calculation time and improve the use rate of computing resources.
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).
文摘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.
