Application of a Robust Multigrid Technique for the Parallel Solution of Initial-Boundary Value Problems

Date

2022-12-01

Author

Martynenko, S.I.
Gökalp, İskender
Bakhtin, V.A.
Karaca, Mehmet
Toktaliev, P.D.
Semenev, P.A.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

153
views

0
downloads

This article is devoted to the construction of a parallel multigrid algorithm for the numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on a robust multigrid technique (RMT). A distinctive feature of the proposed algorithm is the possibility of the parallel solution of initial-boundary value problems and initial-boundary value problems in a unified manner involving 3m independent computers (threads, if the OpenMP parallelization technology is used), m = 1, 2, 3, …. Coarse grids are built only in space, the number of grid levels depends on the conditionality of the coefficient matrix of the resulting system of linear algebraic equations (SLAEs). The Seidel method with the point ordering of the unknowns is used as a smoothing procedure for solving the initial-boundary value problem for a heat equation with constant coefficients. A description of the algorithm and the results of the computational experiments performed using the OpenMP technology are given.

Subject Keywords

initial-boundary value problems, multigrid methods, parallel computing

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85141197142&origin=inward
https://hdl.handle.net/11511/101562

Journal

Mathematical Models and Computer Simulations

DOI

https://doi.org/10.1134/s2070048222060096

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

Solution of initial and boundary value problems by the variational iteration method Altintan, D.; Uğur, Ömür (2014-03-15) The Variational Iteration Method (VIM) is an iterative method that obtains the approximate solution of differential equations. In this paper, it is proven that whenever the initial approximation satisfies the initial conditions, vim obtains the solution of Initial Value Problems (IVPs) with a single iteration. By using this fact, we propose a new algorithm for Boundary Value Problems (BVPs): linear and nonlinear ones. Main advantage of the present method is that it does not use Green's function, however, it...
Parallel processing of two-dimensional euler equations for compressible flows Doǧru, K.; Aksel, M.h.; Tuncer, İsmail Hakkı (2008-12-01) A parallel implementation of a previously developed finite volume algorithm for the solution of two-dimensional, unsteady, compressible Euler equations is given. The conservative form of the Euler equations is discretized with a second order accurate, one-step Lax-Wendroff scheme. Local time stepping is utilized in order to accelerate the convergence. For the parallel implementation of the method, the solution domain is partitioned into a number of subdomains to be distributed to separate processors for par...
On Solving the Forward Kinematics of the 6-6 General Parallel Manipulator with an Efficient Evolutionary Algorithm Rolland, Luc; Chandra, Rohitash (2010-07-08) The G3-PCX genetic algorithm is compared with hybrid meta-heuristic approaches for solving the forward kinematics problem of the 6-6 general parallel manipulator. The G3-PCX shows improvements in terms of accuracy, response time and reliability. Several experiments confirm solving the given problem in less than 1 second. It also reports all the 16 unique real solutions which are verified by an exact algebraic method. This opens the way to simulation and certification applications.
Application of ODSA to population calculation Ulukaya, Mustafa; Demirbaş, Kerim; Department of Electrical and Electronics Engineering (2006) In this thesis, Optimum Decoding-based Smoothing Algorithm (ODSA) is applied to well-known Discrete Lotka-Volterra Model. The performance of the algorithm is investigated for various parameters by simulations. Moreover, ODSA is compared with the SIR Particle Filter Algorithm. The advantages and disadvantages of the both algorithms are presented.
A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind Kaya, Ruşen; Taşeli, Hasan (2022-01-01) A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...

Citation Formats

S. I. Martynenko, İ. Gökalp, V. A. Bakhtin, M. Karaca, P. D. Toktaliev, and P. A. Semenev, “Application of a Robust Multigrid Technique for the Parallel Solution of Initial-Boundary Value Problems,” Mathematical Models and Computer Simulations, vol. 14, no. 6, pp. 1002–1010, 2022, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85141197142&origin=inward.