Construction Of Multigrid Solver For 2D Heat Conduction Problem

This research describes the formulation and application of the multigrid method for the 2D heat conduction problem. A Multigrid method (MG) is essentially a matrix solver which is used with another computational method for solving partial differential equation (PDE) such as finite element method...

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Main Author: Azman, Muhammad Aqil
Format: Monograph
Language:English
Published: Universiti Sains Malaysia 2017
Subjects:
Online Access:http://eprints.usm.my/53486/
http://eprints.usm.my/53486/1/Construction%20Of%20Multigrid%20Solver%20For%202D%20Heat%20Conduction%20Problem_Muhammad%20Aqil%20Azman_M4_2017.pdf
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author Azman, Muhammad Aqil
author_facet Azman, Muhammad Aqil
author_sort Azman, Muhammad Aqil
building USM Institutional Repository
collection Online Access
description This research describes the formulation and application of the multigrid method for the 2D heat conduction problem. A Multigrid method (MG) is essentially a matrix solver which is used with another computational method for solving partial differential equation (PDE) such as finite element method (FEM), boundary element method (BEM), finite different method (FDM) etc. The formulation between FEM and MG is used to test the performance of this combination through the solution. The solution involves partial differential equation (PDE) of Poisson equation of 2D heat conduction problem and the solutions solved by using Matlab. The Poisson equation was tested with various types of heat source and the error L2 norm and H1 norm were computed to validate and prove the convergence of the solution. The solution of FEM and FEM-MG were compared and FEM-MG contains two types of smoother Gauss-Siedel and Successive Over Relaxation (SOR). The result shows that the error of L2 and H1 norm in FEM-MG smaller compare to FEM with conventional linear system solver.
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format Monograph
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institution Universiti Sains Malaysia
institution_category Local University
language English
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publishDate 2017
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spelling usm-534862022-07-20T08:56:02Z http://eprints.usm.my/53486/ Construction Of Multigrid Solver For 2D Heat Conduction Problem Azman, Muhammad Aqil T Technology TJ Mechanical engineering and machinery This research describes the formulation and application of the multigrid method for the 2D heat conduction problem. A Multigrid method (MG) is essentially a matrix solver which is used with another computational method for solving partial differential equation (PDE) such as finite element method (FEM), boundary element method (BEM), finite different method (FDM) etc. The formulation between FEM and MG is used to test the performance of this combination through the solution. The solution involves partial differential equation (PDE) of Poisson equation of 2D heat conduction problem and the solutions solved by using Matlab. The Poisson equation was tested with various types of heat source and the error L2 norm and H1 norm were computed to validate and prove the convergence of the solution. The solution of FEM and FEM-MG were compared and FEM-MG contains two types of smoother Gauss-Siedel and Successive Over Relaxation (SOR). The result shows that the error of L2 and H1 norm in FEM-MG smaller compare to FEM with conventional linear system solver. Universiti Sains Malaysia 2017-06-01 Monograph NonPeerReviewed application/pdf en http://eprints.usm.my/53486/1/Construction%20Of%20Multigrid%20Solver%20For%202D%20Heat%20Conduction%20Problem_Muhammad%20Aqil%20Azman_M4_2017.pdf Azman, Muhammad Aqil (2017) Construction Of Multigrid Solver For 2D Heat Conduction Problem. Project Report. Universiti Sains Malaysia, Pusat Pengajian Kejuruteraan Mekanik. (Submitted)
spellingShingle T Technology
TJ Mechanical engineering and machinery
Azman, Muhammad Aqil
Construction Of Multigrid Solver For 2D Heat Conduction Problem
title Construction Of Multigrid Solver For 2D Heat Conduction Problem
title_full Construction Of Multigrid Solver For 2D Heat Conduction Problem
title_fullStr Construction Of Multigrid Solver For 2D Heat Conduction Problem
title_full_unstemmed Construction Of Multigrid Solver For 2D Heat Conduction Problem
title_short Construction Of Multigrid Solver For 2D Heat Conduction Problem
title_sort construction of multigrid solver for 2d heat conduction problem
topic T Technology
TJ Mechanical engineering and machinery
url http://eprints.usm.my/53486/
http://eprints.usm.my/53486/1/Construction%20Of%20Multigrid%20Solver%20For%202D%20Heat%20Conduction%20Problem_Muhammad%20Aqil%20Azman_M4_2017.pdf