A COMPARISON OF SERIAL AND PARALLEL SOLUTIONS OF TWO DIMENSIONAL HEAT CONDUCTION EQUATION

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S. Abbas A. A. Khan B. Shakia

Abstract

We study a comparison of serial and parallel solution of 2D-parabolic heat conduction equation using a Crank-Nicolson method with an Alternating Direction Implicit (ADI) scheme. The two-dimensional Heat equation is applied on a thin rectangular aluminum sheet. The forward difference formula is used for time and an averaged second order central difference formula for the derivatives in space to develop the Crank-Nicolson method. FORTRAN serial codes and parallel algorithms using OpenMP are used. Thomas tridigonal algorithm and parallel cyclic reduction methods are employed to solve the tridigonal matrix generated while solving heat equation. This paper emphasize on the run time of both algorithms and their difference. The results are compared and evaluated by creating GNU-plots (Command-line driven graphing utility).

Article Details

How to Cite
ABBAS, S.; KHAN, A. A.; SHAKIA, B.. A COMPARISON OF SERIAL AND PARALLEL SOLUTIONS OF TWO DIMENSIONAL HEAT CONDUCTION EQUATION. Journal of Mountain Area Research, [S.l.], v. 5, p. 36-42, dec. 2020. ISSN 2518-850X. Available at: <https://journal.kiu.edu.pk/index.php/JMAR/article/view/79>. Date accessed: 13 june 2021.
Section
Mathematical Sciences

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