1D Multigrid Solver For Finite Element Method
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Date
2022-07-24
Authors
Azhar, Mohamad Amiruddin
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
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.