Publication: Multigrid solver for 1D thermoelectric problems
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Date
2023-07-06
Authors
Lee, Soon Aik
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Abstract
Multigrid method is efficient in solving mathematical problems with the combination of the Finite Element Method. However, the application of this combination of methods in solving engineering fiproblemsblem is not common among
researchers. A sample code written in MATLAB programming language was available in GitHthe ub repository, but it is to solve a simple 1D Poisson’s problem with boundary conditions applied. The sample code is modified to solve 1D thermoelectric problem from an article with results that can be used as a reference for validation. The modification sample code is based on the change of governing equations where the stiffness matrix and the load vector are different. Besides the result from the article, a sample ANSYS APDL code is also modified to apply in solving the same thermoelectric problem. The graphs plotted on temperature & voltage distribution along the thermoelectric cooler from the execution of ANSYS APDL code and MATLAB code are compared with the graphs plotted from the article. The trend of all the graphs is the same, however, the values for the result from MATLAB code is significantly different from the other two sources of results. This is due to the assumptions made that only one material is assigned to the whole thermoelectric cooler as it is difficult to consider different types of material in the governing equation of thermoelectric. Therefore, the modified MATLAB code can solve the problem involving thermoelectric cooler.