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Type: Thesis
Title: Staggered and non-staggered time-domain meshless radial point interpolation method in electromagnetics.
Author: Shaterian, Zahra
Issue Date: 2015
School/Discipline: School of Electrical and Electronic Engineering
Abstract: Meshless methods have gained attention recently as a new class of numerical methods for the solution of partial differential equations in various disciplines of computational engineering. This class of methods offers several promising features compared to mesh-based approaches. The principle of domain discretization with arbitrary node distributions allows accurate modeling of complex geometries with fine details. Moreover, an elaborate and time-consuming re-meshing in the grid-based methods can be replaced in meshless counterparts by an adaptive node refinement during the simulation. This can be exploited to enhance solution accuracy or in optimization procedures. In this thesis, the meshless Radial Point Interpolation Method (RPIM) is investigated for application in time-domain computational electromagnetics. The numerical algorithm is based on a combination of locally defined radial and polynomial basis functions and yields a highly accurate local interpolation of field values and associated derivatives based on the values at close neighboring positions. These interpolated partial derivatives are used to solve the partial differential equations. The thesis is firstly focused on the staggered meshless RPIM. The classical implementation of the staggered meshless RPIM in electromagnetics using the first-order Maxwell’s curl equations is described and the update equations for the staggered electric and magnetic fields are shown. To enhance the capability of the algorithm, a novel implementation of the Uniaxial Perfectly Matched Layer (UPML) is introduced. It is shown however that UPML has intrinsically a long-time instability. Therefore, to avoid this instability two loss terms are introduced, which are added to the update equations in the UPML region after almost all the energy from the computational domain is absorbed. Various capabilities of the meshless method are then validated through different numerical examples using staggered node arrangements in the staggered meshless RPIM. However, the generation of a dual node distribution can be computationally costly and restricts the freedom of node positions, which might reduce the potential advantages of the scheme. To overcome this challenge, the thesis next proposes a novel non-staggered algorithm for the meshless RPIM based on a magnetic vector potential technique. In this method instead of solving Maxwell’s curl equations for the electric and magnetic fields, the wave equation for the magnetic vector potential is solved. Therefore, a single set of nodes can be used to discretize the computational domain. Importantly in the proposed implementation, solving the second-order vector potential wave equation intrinsically enforces the divergence-free property of the electric and magnetic fields and the computational effort associated with the generation of a dual node distribution is avoided. In this part of the thesis, a hybrid algorithm is further proposed to implement staggered perfectly matched layers in the non-staggered RPIM framework. The properties of the proposed non-staggered RPIM are evaluated through several numerical examples both in 2D and 3D implementations. In the last part of the thesis, the staggered and non-staggered implementations of meshless RPIM are directly compared in terms of efficiency and accuracy. It is shown that the non-staggered meshless RPIM not only bypasses the requirement of the dual node distribution, but also suppresses the spurious solutions observed in the staggered implementation. The results of this research show the capability of meshless RPIM for being used efficiently in time-domain computational electromagnetics.
Advisor: Fumeaux, Christophe
Kaufmann, Thomas
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2015
Keywords: computational electromagnetics; time domain methods; meshless methods; radical point interpolation method
Provenance: This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at:
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