Construction Of Multigrid Solver For 2D Heat Conduction Problem - Azman, Muhammad Aqil (Universiti Sains Malaysia, 2017)
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.