The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2018-02-01
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| Series: | International Journal of Applied Mechanics and Engineering |
| Subjects: | |
| Online Access: | https://www.ijame-poland.com/The-Effect-of-Multigrid-Parameters-in-a-3D-Heat-Diffusion-Equation,167005,0,2.html |
| _version_ | 1797750505837953024 |
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| author | F. De Oliveira S.R. Franco M.A. Villela Pinto |
| author_facet | F. De Oliveira S.R. Franco M.A. Villela Pinto |
| author_sort | F. De Oliveira |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:34:43Z |
| format | Article |
| id | doaj.art-a31e51e7bf6841448f04fe734966bd00 |
| institution | Directory Open Access Journal |
| issn | 1734-4492 2353-9003 |
| language | English |
| last_indexed | 2024-03-12T16:34:43Z |
| publishDate | 2018-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | International Journal of Applied Mechanics and Engineering |
| spelling | doaj.art-a31e51e7bf6841448f04fe734966bd002023-08-08T14:58:26ZengUniversity of Zielona GóraInternational Journal of Applied Mechanics and Engineering1734-44922353-90032018-02-0123121322110.1515/ijame-2018-0012167005The Effect of Multigrid Parameters in a 3D Heat Diffusion EquationF. De Oliveira0S.R. Franco1M.A. Villela Pinto2State University of Ponta Grossa, Department of Mathematics and Statistics Ponta Grossa – PR, BrazilState University of Central West, Department of Mathematics Irati – PR, BrazilFederal University of Paraná, Department of Mechanical Engineering , Curitiba – PR, BrazilThe 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.https://www.ijame-poland.com/The-Effect-of-Multigrid-Parameters-in-a-3D-Heat-Diffusion-Equation,167005,0,2.htmlmultigridfinite differencepoisson 3dsolversparameters |
| spellingShingle | F. De Oliveira S.R. Franco M.A. Villela Pinto The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation International Journal of Applied Mechanics and Engineering multigrid finite difference poisson 3d solvers parameters |
| title | The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation |
| title_full | The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation |
| title_fullStr | The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation |
| title_full_unstemmed | The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation |
| title_short | The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation |
| title_sort | effect of multigrid parameters in a 3d heat diffusion equation |
| topic | multigrid finite difference poisson 3d solvers parameters |
| url | https://www.ijame-poland.com/The-Effect-of-Multigrid-Parameters-in-a-3D-Heat-Diffusion-Equation,167005,0,2.html |
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