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

2021 ◽  
Author(s):  
Qigang Liang ◽  
Xuejun Xu
Keyword(s):  
Eigenvalue Problem ◽  
Davidson Method

ON SOLVING ENERGY-DEPENDENT PARTITIONED REAL SYMMETRIC MATRIX EIGENVALUE PROBLEM BY A PARALLEL GENETIC ALGORITHM

2008 ◽  
Vol 07 (06) ◽  
pp. 1103-1120
Author(s):  
RAHUL SHARMA ◽  
SUBHAJIT NANDY ◽  
S. P. BHATTACHARYYA
Keyword(s):  
Genetic Algorithm ◽  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Parallel Genetic Algorithm ◽  
Real Symmetric Matrix ◽  
Advantages And Disadvantages ◽  
Davidson Method ◽  
Energy Dependent ◽  
Parallel Ga ◽  
Serial Mode

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.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
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.

On eigenvalue problem of the Laplace operators for ellipsoidal areas

2018 ◽  
Vol 2018 (1) ◽  
pp. 146-154
Author(s):  
D.G. Rakhimov ◽  
◽  
Sh.M. Suyarov ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Laplace Operators
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