Two Classes of Vector Domain Decomposition Schemes for Time-Dependent Problems with Overlapping Subdomains

2018 ◽  
pp. 85-92
Author(s):  
Petr N. Vabishchevich
Keyword(s):  
Domain Decomposition ◽  
Time Dependent ◽  
Time Dependent Problems ◽  
Decomposition Schemes

scholarly journals Coupling Parareal with Non-Overlapping Domain Decomposition Method

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Rim GUETAT
Keyword(s):  
Domain Decomposition ◽  
Convergence Analysis ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Time Dependent ◽  
Interface Problem ◽  
Time Interval ◽  
Overlapping Domain Decomposition ◽  
Time Dependent Problems

In this paper, we present a new parallel algorithm for time dependent problems based on coupling parareal with non-overlapping domain decomposition method in order to increase parallelism in time and in space. For this we focus on the iterative methods of parallization in space to solve the interface problem like Neumann-Neumann method. In the new algorithm, the coarse temporel propagator is defined on the global domain and the Neumann-Neumann method is chosen as a fine propagator with a few iterations. We present the rigorous convergence analysis of the new coupled algorithm on bounded time interval. Numerical experiments illustrate the performance of this new algorithm and confirm our analysis. RÉSUMÉ. Dans ce papier, nous présentons un nouvel algorithme parallèle pour les problèmes dé-pendant du temps basé sur le couplage du pararéel avec les méthodes de décomposition de domaine sans recouvrement afin d'augmenter le parallélisme dans le temps et l'espace. Nous nous concen-trons sur les méthodes itératives de parallélisation en espace pour résoudre le problème d'interface par la méthode de Neumann-Neumann. Dans ce nouvel algorithme, le propagateur grossier est dé-finie sur le domaine global et la méthode de Neumann-Neumann est choisi pour le propagateur fin avec quelques itérations. Nous présentons l'analyse rigoureuse de convergence du nouvel algorithme couplé sur un intervalle de temps borné. Des expèriences numériques illustrent les performances de ce nouvel algorithme et confirment notre analyse. Dans ce papier, nous présentons un nouvel algorithme parallèle pour les problèmes dépendantdu temps basé sur le couplage du pararéel avec les méthodes de décomposition de domainesans recouvrement afin d’augmenter le parallélisme dans le temps et l’espace. Nous nous concentronssur les méthodes itératives de parallélisation en espace pour résoudre le problème d’interfacepar la méthode de Neumann-Neumann. Dans ce nouvel algorithme, le propagateur grossier est définiesur le domaine global et la méthode de Neumann-Neumann est choisi pour le propagateur finavec quelques itérations. Nous présentons l’analyse rigoureuse de convergence du nouvel algorithmecouplé sur un intervalle de temps borné. Des expèriences numériques illustrent les performances dece nouvel algorithme et confirment notre analyse.

Domain Decomposition Methods With Overlapping Subdomains For The Time-Dependent Problems Of Mathematical Physics

2008 ◽  
Vol 8 (4) ◽  
pp. 393-405 ◽  
Author(s):  
P.N. VABISHCHEVICH
Keyword(s):  
Domain Decomposition ◽  
Data Exchange ◽  
Mathematical Physics ◽  
Decomposition Methods ◽  
Time Dependent ◽  
Parallel Computer ◽  
Approximation Schemes ◽  
Domain Decomposition Methods ◽  
Additive Schemes ◽  
Time Dependent Problems

AbstractAt the present time, the domain decomposition methods are considered as the most promising ones for parallel computer systems. Nowadays success is attained mainly in solving approximately the classical boundary value problems for second-order elliptic equations. As for the time-dependent problems of mathematical physics, there are, in common use, approaches based on ordinary implicit schemes and implemented via iterative methods of the domain decomposition. An alternative technique is based on the non-iterative schemes (region-additive schemes). On the basis of the general theory of additive schemes a wide class of difference schemes (alternative directions, locally one-dimensional, factorized schemes, summarized approximation schemes, vec-tor additive schemes, etc.) as applied to the domain decomposition technique for time-dependent problems with synchronous and asynchronous implementations has been investigated. For nonstationary problems with self-adjoint operators, we have considered three dif-ferent types of decomposition operators corresponding to the Dirichlet and Neumann conditions on the subdomain boundaries. General stability conditions have been obtained for the region-additive schemes. We focused on the accuracy of domain decom-position schemes. In particular, the dependence of the convergence rate on the width of subdomain overlapping has been investigated as the primary property. In the present paper, new classes of domain decomposition schemes for nonstationary problems, based on the subdomain overlaping and minimal data exchange in solving problems in subdomains, have been constructed.

Domain decomposition for time-dependent problems using radial based meshless methods

2006 ◽  
Vol 23 (1) ◽  
pp. 38-59 ◽  
Author(s):  
Phani P. Chinchapatnam ◽  
K. Djidjeli ◽  
Prasanth B. Nair
Keyword(s):  
Domain Decomposition ◽  
Meshless Methods ◽  
Time Dependent ◽  
Time Dependent Problems

Parallelizing implicit algorithms for time-dependent problems by parabolic domain decomposition

1993 ◽  
Vol 8 (2) ◽  
pp. 151-166 ◽  
Author(s):  
M. Israeli ◽  
L. Vozovoi ◽  
A. Averbuch
Keyword(s):  
Domain Decomposition ◽  
Time Dependent ◽  
Time Dependent Problems
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