An Improved Adaptive Mesh Reinforced Algorithm for the Numerical Simulation of Electrostatics Poisson's Equation (MS(M)Thesis) (Record no. 62678)

MARC details
000 -LEADER
fixed length control field 03188nam a2200157Ia 4500
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name 13MSM12
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name Imran Ali Kanhio
-- 13MSM12
-- Supervisor Dr. Shakeel Ahmed Kambho
245 #3 - TITLE STATEMENT
Title An Improved Adaptive Mesh Reinforced Algorithm for the Numerical Simulation of Electrostatics Poisson's Equation (MS(M)Thesis)
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher QUEST
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Year of publication 2018
300 ## - PHYSICAL DESCRIPTION
Number of Pages 41
500 ## - GENERAL NOTE
General note ABSTRACT<br/><br/>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. <br/><br/><br/><br/><br/><br/><br/>
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name Department of Mathematics & Statistics
856 ## - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://tinyurl.com/y9b87wa8
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Thesis and Dissertation
Holdings
Withdrawn status Lost status Home library Current library Date acquired Accession Number Koha item type
    Research Section Research Section 22/10/2018 MP/35-381 Thesis and Dissertation
    Research Section Research Section 26/02/2019 MP/38-412 Thesis and Dissertation