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Fictitious domain and domain decomposition methods
Russian Journal of Numerical Analysis and Mathematical Modelling, 1986Summary: The fictitious domains and domain decomposition methods are treated as iterative methods in subspaces, developed for solving the systems of linear algebraic equations. The first part of the paper is devoted to the algebraic theory of these two methods, and the second part to their application to solving large systems of grid equations ...
Marchuk, G. I. +2 more
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2002
Domain decomposition is a major focus of contemporary research in numerical analysis of partial differential equations. Among the reasons for considering domain decomposition are: parallel computing, modeling of different physical phenomena in different subregions and complicated geometries, and its solid and elegant theoretical foundation.
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Domain decomposition is a major focus of contemporary research in numerical analysis of partial differential equations. Among the reasons for considering domain decomposition are: parallel computing, modeling of different physical phenomena in different subregions and complicated geometries, and its solid and elegant theoretical foundation.
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2002
The domain decomposition method for the solution of differential problems consists of dividing the computational domain into a set of subdomains in which the solution is calculated by taking into account some transmission conditions at the interfaces between the subdomains.
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The domain decomposition method for the solution of differential problems consists of dividing the computational domain into a set of subdomains in which the solution is calculated by taking into account some transmission conditions at the interfaces between the subdomains.
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Heterogeneous Domain Decomposition Methods
1999Abstract In this chapter we address the case of heterogeneous domain decomposition, arising whenever, in the approximation of certain physical phenomena, two different kinds of (initial-) boundary value problems hold within two disjoined subregions of the computational domain.
Alfio Quarteroni, Alberto Valli
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Symbolic Techniques for Domain Decomposition Methods
2013Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today's standard applications, it is necessary to rely on iterative Krylov methods ...
Cluzeau, Thomas +3 more
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Domain decomposition methods for CAD
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999Summary: Constructive solid geometry in CAD leads to domain decompositions which are based on primitive shapes, as briefly explained in the introduction below. A special role is played by ``holes'', which can be viewed in several different ways. We combine this remark with the method of virtual controls. In a previous note [the authors, ibid.
Lions, Jacques-Louis, Pironneau, Olivier
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2014
In the previous chapters we have concentrated on the application and theory of spectral methods for problems in simple domains. There have been a number of recent developments on the use of spectral techniques in more general geometries. The basic idea has been to partition the complete domain of the problem into several subdomains.
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In the previous chapters we have concentrated on the application and theory of spectral methods for problems in simple domains. There have been a number of recent developments on the use of spectral techniques in more general geometries. The basic idea has been to partition the complete domain of the problem into several subdomains.
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Domain Decomposition Methods for Compressible Flows
1999In these notes we consider systems of hyperbolic equations and their reformulation in the framework of multi-domain partition of the computational domain.
A. Quarteroni, Valli, Alberto
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Sinc methods for domain decomposition
Applied Mathematics and Computation, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lybeck, Nancy J., Bowers, Kenneth L.
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Domain Decomposition with Nesterov’s Method
2014We apply the Nesterov minimization method to the domain decomposition of a Poisson problem. The resulting domain decomposition method can be viewed as a projected gradient method and needs only matrix/vector multiplications. Preliminary numerical experiments show that significant speed-up can be obtained with the method.
Firmin Andzembe +2 more
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