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: | |
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| Format: | Monograph |
| Language: | English |
| Published: |
Universiti Sains Malaysia
2017
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| Subjects: | |
| Online Access: | http://eprints.usm.my/53486/1/Construction%20Of%20Multigrid%20Solver%20For%202D%20Heat%20Conduction%20Problem_Muhammad%20Aqil%20Azman_M4_2017.pdf http://eprints.usm.my/53486/ |
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| Summary: | 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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