ABSTRACT

The accuracy and the convergence of numerical solution by Finite Element Method (FEM) depend on the proper discretization of the computational domain. The computational domain is discretized by using different structures like rectangular elements, quad elements, triangular elements, mapped elements, etc., that produce a mesh where the FEM operates to obtain the solution of the problem. It is often a question of interest that how to choose a mesh before finding the more accurate numerical simulation? In most of the cases, fine enough mesh gives accurate answers but the uniform mesh refinement with high resolution lead to an impractical solution time because of redundant computations. Consequently, to reduce the error and to achieve fast convergence a technique of local refinement commonly known as Adaptive Mesh Refinement (AMR) is applied over some boundaries of interest or subsets of the domain. This research is aimed at the formulation of an adaptive mesh refinement algorithm with reduced error is proposed. The main idea is to optimize the number of triangular elements and their size near the boundaries of interest. For testing and implementation the model problem was chosen as electrostatic Poisson's equation applied on a prototype of capacitor. First the model problem was solved by 0-level mesh refinements using FEM and then was solved analytically for the purpose of comparison and validation. It was found that the highest errors exist near the tips and sharp edges of electrode plates. Then an existing Adaptive Mesh Refinement (AMR) was used to reproduce the results for bench marking purpose. After understanding the Benchmark AMR the regions of interest in the computational domain were located by identifying the nodes with highest errors greater than the predefined error tolerance. It was found that the proposed algorithm has improved convergence rate. The computational time (sec) taken by proposed AMR is also reduced as compared to Benchmark AMR and the O­ level FEM. However, for the extremely fine meshes the computational time is higher than the Benchmark AMR but lower than the 0-level FEM. It is because of the high resolution of points in some selected regions and increased steps in the algorithms. Besides all the differences the improvement can be obtained in terms of error which is decreasing with respect to each refinement as compared to 0-level FEM and benchmark AMR. The numerical simulation of capacitor enables to investigate and improve the performance of capacitors. Hence, the proposed research will enhance the understanding and feasibility of using improved AMR in FEM with increasing accuracy.