Convergence of the grid method in the eigenvalue problem for the Helmholtz operator in a right triangle

Yu. I. Rybak

doi:10.1007/bf01229594

Convergence of the grid method in the eigenvalue problem for the Helmholtz operator in a right triangle

Journal of Soviet Mathematics ◽

10.1007/bf01229594 ◽

1993 ◽

Vol 66 (3) ◽

pp. 2263-2267

Author(s):

Yu. I. Rybak

Keyword(s):

Eigenvalue Problem ◽

Grid Method ◽

Helmholtz Operator

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A Two-Grid Method of Nonconforming Element Based on the Shifted-Inverse Power Method for the Steklov Eigenvalue Problem

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.694-697.2918 ◽

2013 ◽

Vol 694-697 ◽

pp. 2918-2921

Author(s):

Hai Bi

Keyword(s):

Eigenvalue Problem ◽

High Efficiency ◽

Grid Method ◽

Inverse Power ◽

Power Method ◽

Discretization Scheme ◽

Nonconforming Element ◽

Steklov Eigenvalue ◽

Steklov Eigenvalue Problem ◽

Numer Anal

This paper establishes a new kind of two-grid discretization scheme of nonconforming Crouzeix-Raviart element based on the shifted-inverse power method for the Steklov eigenvalue problem. The error estimates are provided from the work of Yang and Bi (SIAM J. Numer. Anal., 49, pp.1602-1624, 2011). Finally, numerical experiments are reported to illustrate the high efficiency of the two-grid discretization scheme proposed in this paper.

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Compatible rate-of-convergence bounds for the grid method in the eigenvalue problem for the Helmholtz equation in a right triangle

Journal of Soviet Mathematics ◽

10.1007/bf01098601 ◽

1993 ◽

Vol 66 (2) ◽

pp. 2165-2171

Author(s):

Yu. I. Rybak

Keyword(s):

Eigenvalue Problem ◽

Helmholtz Equation ◽

Rate Of Convergence ◽

Grid Method

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A two-grid method of the non-conforming Crouzeix–Raviart element for the Steklov eigenvalue problem

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.04.051 ◽

2011 ◽

Vol 217 (23) ◽

pp. 9669-9678 ◽

Cited By ~ 12

Author(s):

Hai Bi ◽

Yidu Yang

Keyword(s):

Eigenvalue Problem ◽

Grid Method ◽

Steklov Eigenvalue ◽

Steklov Eigenvalue Problem

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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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