scholarly journals On the finite superelement method in the solution of eigenvalue problems

2018 ◽  
pp. 1-20
Author(s):  
Liudmila Glebovna Strakhovskaya
Keyword(s):  
Eigenvalue Problems ◽  
Superelement Method ◽  
Finite Superelement Method

scholarly journals FEDORENKO FINITE SUPERELEMENT METHOD AS SPECIAL GALERKIN APPROXIMATION

2002 ◽  
Vol 7 (1) ◽  
pp. 41-50 ◽  
Author(s):  
M. Galanin ◽  
E. Savenkov
Keyword(s):  
Boundary Value Problem ◽  
Domain Decomposition ◽  
Iterative Methods ◽  
Variational Equation ◽  
Galerkin Approximation ◽  
Decomposition Methods ◽  
Problem Solution ◽  
Domain Decomposition Methods ◽  
Superelement Method ◽  
Finite Superelement Method

In this work we introduce variational equation which natural Petrov‐Galerkin approximation leads to Fedorenko Finite Superelement Method (FSEM). FSEM is considered as Petrov‐Galerkin approximation of the certain problem for traces of boundary‐value problem solution at the boundaries of some subdomains (superelements). Iterative methods of solution of the same problem are well known domain decomposition methods. Some numerical results are presented.

Fedorenko Finite Superelement Method and Its Applications

2001 ◽  
Vol 7 (1) ◽  
pp. 3-24
Author(s):  
M. Galanin ◽  
S. Lazareva ◽  
E. Savenkov
Keyword(s):  
Numerical Investigation ◽  
Laplace Equation ◽  
Model Problem ◽  
Theoretical Background ◽  
General Idea ◽  
Superelement Method ◽  
Finite Superelement Method

AbstractThis paper considers the Fedorenko Finite Superelement Method (FSEM) and some of its applications. The general idea, the main theoretical background, and the results of the numerical investigation of the method are presented using the model problem for the Laplace equation. Generalization to some other problems using the general approach suggested by the authors is also considered.

NUMERICAL INVESTIGATION OF THE FINITE SUPERELEMENT METHOD FOR THE 3D ELASTICITY PROBLEMS

2007 ◽  
Vol 12 (1) ◽  
pp. 39-50 ◽  
Author(s):  
Mikhail Galanin ◽  
Mikhail Lazarev ◽  
Evgeny Savenkov
Keyword(s):  
Finite Element ◽  
Numerical Investigation ◽  
Model Problem ◽  
Approximation Technique ◽  
Elasticity Problems ◽  
Efficiency Comparison ◽  
Superelement Method ◽  
3D Elasticity ◽  
Definition Of ◽  
Finite Superelement Method

The results of numerical investigation of the Finite Superelement Method (FSEM) for the solution of 3D elasticity problems are given. A definition of FSEM is proposed, and the general theory is briefly explained. Then the variants of FSEM are considered for the model problem. Their comparative analysis is being carried out. These variants are based on the finite element interpolation techniques on superelements boundaries. FSEM and FEM efficiency comparison is presented for the model problem. Quantative error data are obtained. A certain example of a 3D elasticity problem is considered in conclusion. A notable advantage of a higher degree FSEM approximation technique is illustrated.

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