PROJECTION DOMAIN DECOMPOSITION METHOD

1994 ◽  
Vol 04 (06) ◽  
pp. 773-794 ◽  
Author(s):  
V.I. AGOSHKOV ◽  
E. OVTCHINNIKOV
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Discrete Problem ◽  
The Matrix ◽  
Special Basis ◽  
Projection Approach ◽  
Projection Domain

A domain decomposition method using the projection approach is considered. The original elliptic problem is transformed to a set of analogous problems in subdomains and an abstract equation on the interface between subdomains, the latter being solved using Galerkin projection method with some special basis functions defined on the interface. The condition number of the matrix of the resulting discrete problem is shown to be independent of both the number of basis functions and the coefficients of the original problem. Problems in subdomains can be solved independently with different solvers.

scholarly journals Treatment of Block-Based Sparse Matrices in Domain Decomposition Method

2017 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Abul Mukid Mohammad Mukaddes ◽  
Masao Ogino ◽  
Ryuji Shioya ◽  
Hiroshi Kanayama
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Thermal Convection ◽  
Decomposition Method ◽  
Sparse Matrix ◽  
Domain Decomposition Method ◽  
Parallel Computer ◽  
Element Discretization ◽  
Sparsity Pattern ◽  
The Matrix

Abstract— The domain decomposition method involves the finite element solution of problems in the parallel computer. The finite element discretization leads to the solution of large systems of linear equation whose matrix is naturally sparse. The use of proper storing techniques for sparse matrix is fundamental especially when dealing with large scale problems typical of industrial applications. The aim of this research is to review the sparsity pattern of the matrices originating from the discretization of the elasto-plastic and thermal-convection problems. Some practical strategies dealing with sparsity pattern in the finite element code of adventure system are recalled. Several efficient storage schemes to store the matrix originating from elasto-plastic and thermal-convection problems have been proposed. In the proposed technique, inherent block pattern of the matrix is exploited to locate the matrix element. The computation in the high performance computer shows better performance compared to the conventional skyline storage method used by the most of the researchers.

scholarly journals Fast Integral Equation Solution of Scattering of Multiscale Objects by Domain Decomposition Method with Mixed Basis Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ran Zhao ◽  
Hua Peng Zhao ◽  
Zai-ping Nie ◽  
Jun Hu
Keyword(s):  
Integral Equation ◽  
Domain Decomposition ◽  
Mesh Generation ◽  
Electromagnetic Scattering ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Equation Solution ◽  
Nonoverlapping Domain Decomposition ◽  
Well Posed

Nonconformal nonoverlapping domain decomposition method (DDM) with mixed basis functions is presented to realize fast integral equation solution of electromagnetic scattering of multiscale objects. The original multiscale objects are decomposed into several closed subdomains. The higher order hierarchical vector basis functions are used in the electrically large smooth subdomains to significantly reduce the number of unknowns, while traditional Rao-Wilton-Glisson basis functions are used for subdomains with tiny structures. A well-posed matrix is successfully derived by the present DDM. Besides, the nonconformal property of DDM allows flexible mesh generation for complicated objects. Numerical results are presented to validate the proposed method and illustrate its advantages.

Domain Decomposition Method for the Variational Inequality of the Second Kind

2012 ◽  
Vol 542-543 ◽  
pp. 1353-1356
Author(s):  
Jun Hui Zhu ◽  
Chun Rui Cheng
Keyword(s):  
Variational Inequality ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Optimization Problem ◽  
Domain Decomposition Method ◽  
Discrete Problem ◽  
Overlapping Domain Decomposition

Domain decomposition method for solving the discrete problem of the second kind of variational inequality is considered. The variational inequality is reformulated as an equivalent optimization problem. Then the overlapping domain decomposition method is proposed. The convergence of the methods is obtained.

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