A locking‐free shifted inverse iteration based on multigrid discretization for the elastic eigenvalue problem

2021 ◽  
Author(s):  
Xuqing Zhang ◽  
Yidu Yang ◽  
Yu Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Iteration

scholarly journals A Multilevel Correction Scheme for the Steklov Eigenvalue Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Qichao Zhao ◽  
Yidu Yang ◽  
Hai Bi
Keyword(s):  
Theoretical Analysis ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Inverse Iteration ◽  
Correction Technique ◽  
Correction Scheme ◽  
Multiple Eigenvalues ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

Combining the correction technique proposed by Lin and Xie and the shifted inverse iteration, a multilevel correction scheme for the Steklov eigenvalue problem is proposed in this paper. The theoretical analysis and numerical experiments indicate that the scheme proposed in this paper is efficient for both simple and multiple eigenvalues of the Steklov eigenvalue problem.

scholarly journals Smoothed-Adaptive Perturbed Inverse Iteration for Elliptic Eigenvalue Problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Stefano Giani ◽  
Luka Grubišić ◽  
Luca Heltai ◽  
Ornela Mulita
Keyword(s):  
Eigenvalue Problem ◽  
Eigenvalue Problems ◽  
Numerical Linear Algebra ◽  
Three Dimensions ◽  
Iteration Algorithm ◽  
Polygonal Domain ◽  
Inverse Iteration ◽  
Subspace Iteration ◽  
Laplace Eigenvalue ◽  
Refinement Strategy

Abstract We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is motivated by the analysis of inexact (perturbed) inverse iteration algorithms in numerical linear algebra. We couple the perturbed inverse iteration approach with mesh refinement strategy based on residual estimators. We demonstrate our approach on model problems in two and three dimensions.

scholarly journals A Type of Multigrid Method Based on the Fixed-Shift Inverse Iteration for the Steklov Eigenvalue Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Feiyan Li ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Error Estimates ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Inverse Iteration ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem

For the Steklov eigenvalue problem, we establish a type of multigrid discretizations based on the fixed-shift inverse iteration and study in depth its a priori/a posteriori error estimates. In addition, we also propose an adaptive algorithm on the basis of the a posteriori error estimates. Finally, we present some numerical examples to validate the efficiency of our method.

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