Open AccessA COMPARISON OF SERIAL AND PARALLEL SOLUTIONS OF TWO DIMENSIONAL HEAT CONDUCTION EQUATION
Author(s) -
Syed Comail Abbas,
Aurangzeb Khan,
B. Shakia
Publication year - 2020
Publication title -
journal of mountain area research
Language(s) - English
Resource type - Journals
eISSN - 2518-850X
pISSN - 2518-8496
DOI - 10.53874/jmar.v5i0.79
Subject(s) - crank–nicolson method , alternating direction implicit method , fortran , heat equation , thermal conduction , mathematics , crank , finite difference method , matrix (chemical analysis) , mathematical analysis , computer science , geometry , thermodynamics , physics , materials science , cylinder , composite material , operating system
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).