arXiv subjects

Chunguang You

Publications and source records attributed to Chunguang You.

3 recordsLinked to original sources

arXiv2017

Energy Error Estimates of Subspace Method and Multigrid Algorithm for Eigenvalue Problems

This paper is to give a new understanding and applications of the subspace projection method for selfadjoint eigenvalue problems. A new error estimate in the energy norm, which is induced by the stiff matrix, of the subspace projection method for eigenvalue problems is given. The relation between error estimates in $L^2$-norm and energy norm is also deduced. Based on this relation, a new type of inverse power method is designed for eigenvalue problems and the corresponding convergence analysis is also provided. Then we present the analysis of the geometric and algebraic multigrid methods for eigenvalue problems based on the convergence result of the new inverse power method.

math.NA↗

arXiv2016

A Small Note About Lower Bound of Eigenvalues

This paper gives a framework to produce the lower bound of eigenvalues defined in a Hilbert space by the eigenvalues defined in another Hilbert space. The method is based on using the max-min principle for the eigenvalue problems.

math.NA↗

arXiv2014

Local and Parallel Finite Element Algorithm Based On Multilevel Discretization for Eigenvalue Problem

A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is transferred to solutions of the eigenvalue problems on the coarsest mesh and a series of solutions of boundary value problems by using the local and parallel algorithm. The computational work in each processor can reach the optimal order. Therefore, this type of multilevel local and parallel method improves the overall efficiency of solving the eigenvalue problem. Some numerical experiments are presented to validate the efficiency of the new method.

math.NA↗