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ORIGINAL PAPER
The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation
1
State University of Ponta Grossa, Department of Mathematics and Statistics Ponta Grossa – PR, Brazil
2
State University of Central West, Department of Mathematics Irati – PR, Brazil
3
Federal University of Paraná Graduate Program in Numerical Methods in Engineering , Curitiba – PR, Brazil
4
Federal University of Paraná, Department of Mechanical Engineering , Curitiba – PR, Brazil
Online publication date: 2018-03-14
Publication date: 2018-02-01
International Journal of Applied Mechanics and Engineering 2018;23(1):213-221
KEYWORDS
ABSTRACT
The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.
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