Parallel algorithms and domain decomposition technologies for solving three-dimensional boundary value problems on quasi-structured grids

2016 ◽  
Keyword(s):  
Parallel Algorithms ◽  
Domain Decomposition ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Structured Grids ◽  
Dimensional Boundary

scholarly journals Parallelization technologies for solving three-dimensional boundary value problems on quasi-structured grids using the CPU+GPU hybrid computing environment

2016 ◽  
pp. 65-71
Author(s):  
И.А. Климонов ◽  
В.Д. Корнеев ◽  
В.М. Свешников
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Computational Domain ◽  
Computing Environment ◽  
Structured Grids ◽  
Hybrid Computing ◽  
Solution Processes ◽  
Dimensional Boundary

При распараллеливании решения трехмерных краевых задач на квазиструктурированных сетках методом декомпозиции расчетной области на подобласти, сопрягаемые без наложения, наиболее трудоемкой вычислительной процедурой является решение краевых подзадач в подобластях. Использование параллелепипедальных квазиструктурированных сеток дает возможность применить для этих целей быстросходящиеся методы переменных направлений. Распараллеливание итерационного процесса по подобластям проводится на CPU в системе MPI, а для решения подзадач в настоящей статье предлагается использовать графические ускорители GPU. Приводятся экспериментальные исследования применения графических ускорителей при решении подзадач методом Писмана-Речфорда. Даются экспериментальные оценки ускорения распараллеливания в гибридной вычислительной среде CPU+GPU по сравнению с расчетами только на CPU. When parallelizing the solution processes of solving three-dimensional boundary value problems on quasi-structured grids by the method of decomposition of the computational domain into subdomains without imposition, the most time consuming computational procedure is a solution of subproblems in subdomains. The application of parallelepiped quasi-structured grids makes it possible to use the rapidly convergent method of alternating directions. The parallelization of iterative processes on subdomains is performed on CPU using MPI. In order to solve the subproblems, we propose to use the graphics accelerators (GPU). Experimental results of using the graphics accelerators to solve the subproblems by Peaceman-Rachford method are discussed. The computational acceleration achieved on the CPU+GPU hybrid computing environment is experimentally estimated compared to using the CPU only.

scholarly journals Acceleration of parallel algorithms for solving three-dimensional boundary value problems on quasi-structured grids

2018 ◽  
pp. 121-129
Author(s):  
И.А. Климонов ◽  
В.Д. Корнеев ◽  
В.М. Свешников
Keyword(s):  
Boundary Value Problems ◽  
Domain Decomposition Method ◽  
Boundary Value ◽  
Three Dimensional ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Structured Grids ◽  
Parallel Solution ◽  
Linear Algebraic Equations ◽  
Dimensional Boundary

Статья посвящена ускорению параллельного решения трехмерных краевых задач методом декомпозиции расчетной области на подобласти, сопрягаемые без наложения. Декомпозиция проводится равномерной параллелепипедальной макросеткой. В каждой подобласти и на границе сопряжения (интерфейсе) строятся свои структурированные подсетки. Объединение этих подсеток образует квазиструктурированную сетку, на которой решается поставленная задача. Распараллеливание решения осуществляется при помощи MPI-технологий. Предложен и экспериментально исследован алгоритм ускорения внешнего итерационного процесса по подобластям для решения системы линейных алгебраических уравнений, аппроксимирующих уравнение Пуанкаре-Стеклова на интерфейсе. Проведены серии численных экспериментов на различных квазиструктурированных сетках и при различных параметрах вычислительных алгоритмов, показывающих ускорение вычислений. This paper is devoted to the acceleration of the parallel solution of three-dimensional boundary value problems by the computational domain decomposition method into subdomains that are conjugated without overlapping. The decomposition is performed by a uniform parallelepipedal macrogrid. In each subdomain and on the interface, some structured subgrids are constructed. The union of these subgrids forms a quasi-structured grid on which the problem is solved. The parallelization is carried out using the MPI-technology. We propose and experimentally study the acceleration algorithm for an external iterative process on subdomains to solve a system of linear algebraic equations approximating the Poincare-Steklov equation on the interface. A number of numerical experiments are carried out on various quasi-structured grids and with various parameters of computational algorithms showing the acceleration of computations.

Solutions to Particular Three-Dimensional Boundary Value Problems of Elastostatics

2013 ◽  
pp. 209-218
Author(s):  
Reza Eslami ◽  
Richard B. Hetnarski ◽  
Jozef Ignaczak ◽  
Naotake Noda ◽  
Naobumi Sumi ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Dimensional Boundary

scholarly journals Remarks on Generation of the Orthogonal Structured Grids

2019 ◽  
pp. 16-26
Author(s):  
S.I. Martynenko
Keyword(s):  
Mathematical Modeling ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Grid Generation ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Structured Grids ◽  
Orthogonal Grid ◽  
Initial Boundary Value

Grid generation techniques have contributed significantly toward the application of mathematical modeling in large-scale engineering problems. The structured grids have the advantage that very robust and parallel computational algorithms have been proposed for solving (initial-)boundary value problems. Orthogonal grids make it possible to simplify an approximation of the differential equations and to increase computation accuracy. Opportunity of the orthogonal structured grid generation for solving two- and three-dimensional (initial-)boundary value problems is analyzed in the article in assumption that isolines or isosurfaces of d (=2,3) functions form this grid. Condition of the isolines/isosurfaces orthogonality is used for formulation of the boundary value problems, the solutions of which will be form the orthogonal grid. A differential substitution is proposed to formulate the boundary value problems directly from the orthogonality condition of the grid. The substitution leads to the general partial differrential equations with undetermined coefficients. In the two-dimensional case, it is shown that the orthogonal grid generation is equivalent to the solution of partial differential equations of either elliptic or hyperbolic type. In three-dimensional domains, an orthogonal grid can be generated only in special cases. The obtained results are useful for mathematical modeling of the complex physicochemical processes in the technical devices

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