A Symmetry-Based Decomposition Approach to Eigenvalue Problems

Authors:
Jun Fang;Xingyu Gao;Aihui Zhou
Affiliations:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China 100190;HPCC, Institute of Applied Physics and Computational Mathematics, Beijing, China 100094;LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China 100190
Venue:
Journal of Scientific Computing
Year:
2013

Citing 7
Cited 0

Symmetry, groups and boundary value problems. A progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry

Computer Methods in Applied Mechanics and Engineering
Boundary value problems with symmetry and their approximation by finite elements

SIAM Journal on Applied Mathematics
Eigenfrequencies of fractal drums

Journal of Computational and Applied Mathematics
Finite element approach for density functional theory calculations on locally-refined meshes

Journal of Computational Physics
Computing eigenfunctions on the Koch Snowflake: A new grid and symmetry

Journal of Computational and Applied Mathematics
First-principles calculations of electron states of a silicon nanowire with 100,000 atoms on the K computer

Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
A Kohn-Sham equation solver based on hexahedral finite elements

Journal of Computational Physics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we propose a decomposition approach to differential eigenvalue problems with Abelian or non-Abelian symmetries. In the approach, we divide the original differential problem into eigenvalue subproblems which require less eigenpairs and can be solved independently. Our approach can be seamlessly incorporated with grid-based discretizations such as finite difference, finite element, or finite volume methods. We place the approach into a two-level parallelization setting, which saves the CPU time remarkably. For illustration and application, we implement our approach with finite elements and carry out electronic structure calculations of some symmetric cluster systems, in which we solve thousands of eigenpairs with millions of degrees of freedom and demonstrate the effectiveness of the approach.