A two-level preconditioned Helmholtz-Jacobi-Davidson method for the Maxwell eigenvalue problem

An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of a serial as well as parallel genetic algorithm (GA). The proposed method is tested on two matrices (up to 2000 × 2000) with an increasing number of processors in a master–slave architecture. A comparison is made with the Jacobi–Davidson method in serial mode as implemented in the JDQZ-package. Different partition sizes are used. Traditionally used Löwdin's method is also tested in both serial and parallel modes. The advantages and disadvantages of the parallel GA-based method in solving the partitioned eigenvalue problem are analyzed.

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Reducing synchronization on the parallel Davidson method for the large sparse, eigenvalue problem

Proceedings of the 1993 ACM/IEEE conference on Supercomputing - Supercomputing '93 ◽

10.1145/169627.169685 ◽

1993 ◽

Cited By ~ 6

Author(s):

A. Stathopoulos ◽

C. F. Fischer

Keyword(s):

Eigenvalue Problem ◽

Davidson Method

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FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRÖDINGER EIGENVALUE PROBLEM

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30132-2 ◽

1994 ◽

Vol 14 (4) ◽

pp. 426-437

Author(s):

Liede Huang ◽

Zhonghuan Xia

Keyword(s):

Eigenvalue Problem ◽

Nonlinear Equations ◽

Fredholm Determinant

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A comparative study of history-based versus vectorized Monte Carlo methods in the GPU/CUDA environment for a simple neutron eigenvalue problem

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo ◽

10.1051/snamc/201404206 ◽

2014 ◽

Cited By ~ 1

Author(s):

Tianyu Liu ◽

Xining Du ◽

Wei Ji ◽

X. George Xu ◽

Forrest B. Brown

Keyword(s):

Monte Carlo ◽

Eigenvalue Problem ◽

Comparative Study ◽

Monte Carlo Methods

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Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2006.11.1.14762 ◽

2006 ◽

Vol 11 (1) ◽

pp. 13-32 ◽

Cited By ~ 10

Author(s):

B. Bandyrskii ◽

I. Lazurchak ◽

V. Makarov ◽

M. Sapagovas

Keyword(s):

Differential Equation ◽

Eigenvalue Problem ◽

Variable Coefficient ◽

Order Differential Equation ◽

Integral Condition ◽

Second Order ◽

Computational Results ◽

Discrete Method ◽

Complex Eigenvalues ◽

Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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