1D Multigrid Solver For Finite Element Method - Azhar, Mohamad Amiruddin (Universiti Sains Malaysia, 2022)
Computational code using the Multigrid Method with the combination of the Finite Element Method to solve a mathematical problem is quite rare in the public domain. Usually, the mathematical problem can be solved using only one of those two methods. A sample of such code written in MATLAB programming language was found in the GitHub repository, where the implemented algorithms are far from optimal. This available algorithm of the Multigrid solver with the Finite Element Method was modified and tested for its performance. Two kinds of computation have been used to determine the performance of the solver. The first one is time simulation. This simulation will determine the time taken for the simulation to complete for every number of elements. The performance of the algorithm for any number of elements can be identified from this simulation. The time test on the algorithm shows the high number of elements, the higher time taken to complete the simulation. However, the algorithm provided by the GitHub repository is less efficient. Therefore, some modifications to the algorithm are made to increase the performance of the solver. The second type is memory simulation. The memory performance was tested by determining the value of memory used for every number of elements. However, the data produced is insufficient and inaccurate. Therefore, the performance of the algorithm can not be determined using this parameter. Next, the algorithm was modified by using a new Gauss-Seidel function. The new algorithm also has been tested using time simulation. Then, the result was compared with the result of the time simulation before the modification. The test gives a more significant result than the original algorithm. Therefore, the modification of the algorithm gives a positive impact on solver efficiency.