A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem.The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy...A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem.The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy.Error estimates and optimal convergence for the proposed method are proved.Numerical examples show that the proposed method inherits the advantages of both ingredients and can compute low regularity eigenfunctions effectively.展开更多
This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique.A high order lower bound can be obtained at a relatively low cost via the proposed me...This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique.A high order lower bound can be obtained at a relatively low cost via the proposed method.The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions.Numerical examples are presented to validate the theoretical analysis.展开更多
基金supported in part by the Doctoral Scientific Research Foun-dation of Guizhou Normal University(No.GZNUD[2018]33)Guizhou Province Science and Technology Plan Project(No.[2018]5769)+2 种基金supported in part by the National Natural Science Foundation of China under grants NSFC 11471031,NSFC 91430216,NSAF U1530401the US National Science Foundation under grant DMS-1419040supported in part by National Science Foundation under grant DMS-1521555.
文摘A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem.The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy.Error estimates and optimal convergence for the proposed method are proved.Numerical examples show that the proposed method inherits the advantages of both ingredients and can compute low regularity eigenfunctions effectively.
基金The work of Q.Zhai was partially supported by China Postdoc total Science Foundation(2018M640013,2019T120008)The work of X.Hu was partially supported by NSF grant(DMS-1620063)+1 种基金The work of R.Zhang was supported in part by China Natural National Science Foundation(91630201,11871245,11771179)by the Program for Cheung Kong Scholars of Ministry of Education of China,Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education,Jilin University,Changchun,130012,P.R.China.
文摘This paper proposes and analyzes a new weak Galerkin method for the eigenvalue problem by using the shifted-inverse power technique.A high order lower bound can be obtained at a relatively low cost via the proposed method.The error estimates for both eigenvalue and eigenfunction are provided and asymptotic lower bounds are shown as well under some conditions.Numerical examples are presented to validate the theoretical analysis.
