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
We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of fr...We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of freedom and their“immediate”neighbors.In the context of lowest order conforming finite element approximations,we present a unified proof for the convergence of adaptive multigrid V-cycle algorithms.The theory applies to any hierarchical tetrahedral meshes with uniformly bounded shape-regularity measures.The convergence rates for both problems are uniform with respect to the number of mesh levels and the number of degrees of freedom.We demonstrate our convergence theory by two numerical experiments.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supported in part by the National Magnetic Confinement Fusion Science Program(Grant No.2011GB105003)the NSF of China under the grants 91130004,11071116,and 10971096+1 种基金supported in part by China NSF under the grants 11031006 and 11171334the Funds for Creative Research Groups of China(Grant No.11021101).
文摘We consider the convergence theory of adaptive multigrid methods for secondorder elliptic problems and Maxwell’s equations.The multigrid algorithm only performs pointwise Gauss-Seidel relaxations on new degrees of freedom and their“immediate”neighbors.In the context of lowest order conforming finite element approximations,we present a unified proof for the convergence of adaptive multigrid V-cycle algorithms.The theory applies to any hierarchical tetrahedral meshes with uniformly bounded shape-regularity measures.The convergence rates for both problems are uniform with respect to the number of mesh levels and the number of degrees of freedom.We demonstrate our convergence theory by two numerical experiments.
