Multigrid Solver for 2D Heat Conduction Problems

摘要

As analytical solutions to heat transfer problems are difficult to obtain. Computational methods are presented as important analysis tools but conventional computational methods like Gauss-Seidel iteration are slow to converge. Therefore, a multigrid solver is introduced to address this issue. This report covers the two-dimensional rectangular heat conduction being solved using the finite-difference method and accelerated by the multigrid method. A brief explanation of multigrid will be presented. The result obtained from the analytical solutions were used as the baseline for comparison with the multigrid method. Once the results from the multigrid are validated, the single-grid method (Gauss-Seidel) is compared with the multigrid method in term of convergence rate and accuracy of results.