Numerical Solution of Helmholtz Equation by the Modified Hopfield Finite Difference Techniques

被引：13

作者：

Dehghan, Mehdi ^{[1
]}

Nourian, Mojtaba ^{[1
]}

Menhaj, Mohammad B. ^{[2
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran

[2] Amirkabir Univ Technol, Dept Elect Engn, Tehran 15914, Iran

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 25卷 / 03期

关键词：

finite difference techniques; Helmholtz equation; modified Hopfield neural networks; 2-DIMENSIONAL DIFFUSION; CONTROL PARAMETER; NETWORKS; SUBJECT;

D O I：

10.1002/num.20366

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One property of the Hopfield neural networks is the monotone minimization of energy as time proceeds. In this article, this property is applied to minimize the energy functions obtained by finite difference techniques of the Helmholtz-equation. The mathematical representation and correlation between finite difference techniques and modified Hopfield neural networks of the Helmholtz equation are presented. Significant advantages of the above method are its parallel, robust, easy programming nature, and ability of direct hardware implementation. Results of numerical simulations are described and analyzed to demonstrate the method. The results obtained using the proposed method show a very good agreement with theoretical and numerical solutions. (C) 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 25: 637-656, 2009

引用

页码：637 / 656

页数：20

共 50 条

[1] Optimization of a Finite-Difference Scheme for Numerical Solution of the Helmholtz Equation
Kostin, V. I.
Solov'ev, S. A.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2020, 60 (04) : 641 - 650
[2] Optimization of a Finite-Difference Scheme for Numerical Solution of the Helmholtz Equation
V. I. Kostin
S. A. Solov’ev
[J]. Computational Mathematics and Mathematical Physics, 2020, 60 : 641 - 650
[3] Preconditionning techniques for the solution of the Helmholtz equation by the finite element method
Kechroud, R
Soulaimani, A
Saad, Y
[J]. COMPUTATIONAL SCIENCE AND ITS APPLICATIONS - ICCSA 2003, PT 2, PROCEEDINGS, 2003, 2668 : 847 - 858
[4] Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
Kechroud, R
Soulaimani, A
Saad, Y
Gowda, S
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2004, 65 (4-5) : 303 - 321
[5] A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers' equation
Oruc, O.
Bulut, F.
Esen, A.
[J]. JOURNAL OF MATHEMATICAL CHEMISTRY, 2015, 53 (07) : 1592 - 1607
[6] A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers’ equation
Ö. Oruç
F. Bulut
A. Esen
[J]. Journal of Mathematical Chemistry, 2015, 53 (7) : 1592 - 1607
[7] On numerical solution of the complex Helmholtz equation
Il'in, V. P.
Petukhov, A. V.
[J]. RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2007, 22 (01) : 19 - 37
[8] A NOTE ON RICHARDSON SOLUTION OF THE HEAT EQUATION BY FINITE DIFFERENCE TECHNIQUES
KAPLAN, S
OBRIEN, G
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 55 (05) : 519 - 519
[9] ON THE NUMERICAL-SOLUTION OF HELMHOLTZ-EQUATION BY THE FINITE-ELEMENT METHOD
AZIZ, AK
WERSCHULZ, A
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (05) : 681 - 686
[10] Optimal finite-difference sub-gridding techniques applied to the Helmholtz equation
Nehrbass, JW
Lee, R
[J]. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2000, 48 (06) : 976 - 984

← 1 2 3 4 5 →