scholarly journals Issues of parallel software development for the domain decomposition methods

2018 ◽  
pp. 219-229
Author(s):  
Я.Л. Гурьева ◽  
Д.В. Перевозкин
Keyword(s):  
Software Development ◽  
Domain Decomposition ◽  
Data Exchange ◽  
Model Problem ◽  
Computation Time ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Index Sets ◽  
Parallel Software ◽  
Parallel Software Development

Рассматриваются различные аспекты разработки параллельного программного обеспечения для метода декомпозиции области: использование технологии MPI-программирования для кластерных систем, точки выбора при проектировании параллельных программ методов декомпозиции области, необходимость реализации действия матрицы без явного ее представления, работа с множествами индексов при программной реализации операторов ограничения и продолжения, а также при обмене данными между подобластями. На ряде численных экспериментов для модельной задачи исследуются вопросы наилучшего выбора конфигурации запуска исполняемой программы на кластере для минимизации времени расчета и предлагается стратегия проведения серии вычислительных экспериментов. Various aspects of parallel software development for the domain decomposition methods are considered: the application of MPI programming technology for cluster systems, the choice points in the design of parallel programs for the domain decomposition methods, the need to implement a matrix action without its explicit representation, the work with index sets in the software implementation of restriction and continuation operators as well as in the data exchange between subdomains. On a series of numerical experiments for a model problem, the questions of the best choice of the configuration of launching an executable program on a cluster are studied to minimize the computation time and a strategy for performing such experiments is proposed.

scholarly journals Finite Element Tearing and Interconnecting Method and its Algorithms for Parallel Solution of Magnetic Field Problems

2013 ◽  
Vol 3 (1) ◽  
pp. 25-30
Author(s):  
Dániel Marcsa ◽  
Miklós Kuczmann
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Domain Decomposition ◽  
Data Exchange ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Engineering Practice ◽  
Domain Decomposition Methods ◽  
Parallel Solution ◽  
Solution Algorithms

Abstract Because of the exponential increase of computational resource requirement for numerical field simulations of more and more complex physical phenomena and more and more complex large problems in science and engineering practice, parallel processing appears to be an essential tool to handle the resulting large-scale numerical problems. One way of parallelization of sequential (singleprocessor) finite element simulations is the use of domain decomposition methods. Domain decomposition methods (DDMs) for parallel solution of linear systems of equations are based on the partitioning of the analyzed domain into sub-domains which are calculated in parallel while doing appropriate data exchange between those sub-domains. In this case, the non-overlapping domain decomposition method is the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method. This paper describes one direct solver and two parallel solution algorithms of FETI method. Finally, comparative numerical tests demonstrate the differences in the parallel running performance of the solvers of FETI method. We use a single-phase transformer and a three-phase induction motor as twodimensional static magnetic field test problems to compare the solvers

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.

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