Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: This work considers the acceleration of matrix-based computational electromagnetic (CEM) techniques using graphics processing units (GPUs). These massively parallel processors have gained much support since late 2006, with software tools such as CUDA and OpenCL greatly simplifying the process of harnessing the computational power of these devices. As with any advances in computation, the use of these devices enables the modelling of more complex problems, which in turn should give rise to better solutions to a number of global challenges faced at present. For the purpose of this dissertation, CUDA is used in an investigation of the acceleration of two methods in CEM that are used to tackle a variety of problems. The first of these is the Method of Moments (MOM) which is typically used to model radiation and scattering problems, with the latter begin considered here. For the CUDA acceleration of the MOM presented here, the assembly and subsequent solution of the matrix equation associated with the method are considered. This is done for both single and double precision oating point matrices. For the solution of the matrix equation, general dense linear algebra techniques are used, which allow for the use of a vast expanse of existing knowledge on the subject. This also means that implementations developed here along with the results presented are immediately applicable to the same wide array of applications where these methods are employed. Both the assembly and solution of the matrix equation implementations presented result in signi cant speedups over multi-core CPU implementations, with speedups of up to 300x and 10x, respectively, being measured. The implementations presented also overcome one of the major limitations in the use of GPUs as accelerators (that of limited memory capacity) with problems up to 16 times larger than would normally be possible being solved. The second matrix-based technique considered is the Finite Element Method (FEM), which allows for the accurate modelling of complex geometric structures including non-uniform dielectric and magnetic properties of materials, and is particularly well suited to handling bounded structures such as waveguide. In this work the CUDA acceleration of the cutoff and dispersion analysis of three waveguide configurations is presented. The modelling of these problems using an open-source software package, FEniCS, is also discussed. Once again, the problem can be approached from a linear algebra perspective, with the formulation in this case resulting in a generalised eigenvalue (GEV) problem. For the problems considered, a total solution speedup of up to 7x is measured for the solution of the generalised eigenvalue problem, with up to 22x being attained for the solution of the standard eigenvalue problem that forms part of the GEV problem. / AFRIKAANSE OPSOMMING: In hierdie werkstuk word die versnelling van matriksmetodes in numeriese elektromagnetika (NEM) deur die gebruik van grafiese verwerkingseenhede (GVEe) oorweeg. Die gebruik van hierdie verwerkingseenhede is aansienlik vergemaklik in 2006 deur sagteware pakette soos CUDA en OpenCL. Hierdie toestelle, soos ander verbeterings in verwerkings vermoe, maak dit moontlik om meer komplekse probleme op te los. Hierdie stel wetenskaplikes weer in staat om globale uitdagings beter aan te pak. In hierdie proefskrif word CUDA gebruik om ondersoek in te stel na die versnelling van twee metodes in NEM, naamlik die Moment Metode (MOM) en die Eindige Element Metode (EEM). Die MOM word tipies gebruik om stralings- en weerkaatsingsprobleme op te los. Hier word slegs na die weerkaatsingsprobleme gekyk. CUDA word gebruik om die opstel van die MOM matriks en ook die daaropvolgende oplossing van die matriksvergelyking wat met die metode gepaard gaan te bespoedig. Algemene digte lineere algebra tegnieke word benut om die matriksvergelykings op te los. Dit stel die magdom bestaande kennis in die vagebied beskikbaar vir die oplossing, en gee ook aanleiding daartoe dat enige implementasies wat ontwikkel word en resultate wat verkry word ook betrekking het tot 'n wye verskeidenheid probleme wat die lineere algebra metodes gebruik. Daar is gevind dat beide die opstelling van die matriks en die oplossing van die matriksvergelyking aansienlik vinniger is as veelverwerker SVE implementasies. 'n Verselling van tot 300x en 10x onderkeidelik is gemeet vir die opstel en oplos fases. Die hoeveelheid geheue beskikbaar tot die GVE is een van die belangrike beperkinge vir die gebruik van GVEe vir groot probleme. Hierdie beperking word hierin oorkom en probleme wat selfs 16 keer groter is as die GVE se beskikbare geheue word geakkommodeer en suksesvol opgelos. Die Eindige Element Metode word op sy beurt gebruik om komplekse geometriee asook nieuniforme materiaaleienskappe te modelleer. Die EEM is ook baie geskik om begrensde strukture soos golfgeleiers te hanteer. Hier word CUDA gebruik of om die afsny- en dispersieanalise van drie gol eierkonfigurasies te versnel. Die implementasie van hierdie probleme word gedoen deur 'n versameling oopbronkode wat bekend staan as FEniCS, wat ook hierin bespreek word. Die probleme wat ontstaan in die EEM kan weereens vanaf 'n lineere algebra uitganspunt benader word. In hierdie geval lei die formulering tot 'n algemene eiewaardeprobleem. Vir die gol eier probleme wat ondersoek word is gevind dat die algemene eiewaardeprobleem met tot 7x versnel word. Die standaard eiewaardeprobleem wat 'n stap is in die oplossing van die algemene eiewaardeprobleem is met tot 22x versnel.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2007. / The finite element tearing and interconnect(FETI) domain decomposition(DD) method is investigated in terms of the 2D transverse electric(TEz) finite element method(FEM). The FETI is for the first time rigorously derived using the weighted residual framework from which important insights are gained. The FETI is used in a novel way to implement a total-/scattered field decomposition and is shown to give excellent results. The FETI is newly formulated for the time domain(FETI-TD), its feasibility is tested and it is further formulated and tested for implementation on a distributed computer architecture.

This dissertation presents techniques for high-order simulation of electromagnetic fields, particularly for problems involving ships with ferromagnetic hulls and active corrosion-protection systems. A set of numerically constrained hexahedral basis functions for volume integral equation discretization is presented in a method-of-moments context. Test simulations demonstrate the accuracy achievable with these functions as well as the improvement brought about in system conditioning when compared to other basis sets. A general method for converting between a locally-corrected Nyström discretization of an integral equation and a method-of-moments discretization is presented next. Several problems involving conducting and magnetic-conducting materials are solved to verify the accuracy of the method and to illustrate both the reduction in number of unknowns and the effect of the numerically constrained bases on the conditioning of the converted matrix. Finally, a surface integral equation derived from Laplace’s equation is discretized using the locally-corrected Nyström method in order to calculate the electric fields created by impressed-current corrosion protection systems. An iterative technique is presented for handling nonlinear boundary conditions. In addition we examine different approaches for calculating the magnetic field radiated by the corrosion protection system. Numerical tests show the accuracy achievable by higher-order discretizations, validate the iterative technique presented. Various methods for magnetic field calculation are also applied to basic test cases.

<div>The design of advanced integrated circuits (ICs) and systems calls for multiphysics and large-scale modeling and simulation methods. On the one hand, novel devices and materials are emerging in next-generation IC technology, which requires multiphysics modeling and simulation. On the other hand, the ever-increasing complexity of ICs requires more efficient numerical solvers.</div><div><br></div><div>In this work, we propose a multiphysics modeling and simulation algorithm to co-simulate Maxwell's equations, dispersion relation of materials, and Boltzmann equation to characterize emerging new devices in IC technology such as Cu-Graphene (Cu-G) hybrid nano-interconnects. We also develop an unconditionally stable time marching scheme to remove the dependence of time step on space step for an efficient simulation of the multiscaled and multiphysics system. Extensive numerical experiments and comparisons with measurements have validated the accuracy and efficiency of the proposed algorithm. Compared to simplified steady-state-models based analysis, a significant difference is observed when the frequency is high or/and the dimension of the Cu-G structure is small, which necessitates our proposed multiphysics modeling and simulation for the design of advanced Cu-G interconnects. </div><div><br></div><div>To address the large-scale simulation challenge, we develop a new split-field domain-decomposition algorithm amenable for parallelization for solving Maxwell’s equations, which minimizes the communication between subdomains, while having a fast convergence of the global solution. Meanwhile, the algorithm is unconditionally stable in time domain. In this algorithm, unlike prevailing domain decomposition methods that treat the interface unknown as a whole and let it be shared across subdomains, we partition the interface unknown into multiple components, and solve each of them from one subdomain. In this way, we transform the original coupled system to fully decoupled subsystems to solve. Only one addition (communication) of the interface unknown needs to be performed after the computation in each subdomain is finished at each time step. More importantly, the algorithm has a fast convergence and permits the use of a large time step irrespective of space step. Numerical experiments on large-scale on-chip and package layout analysis have demonstrated the capability of the new domain decomposition algorithm. </div><div><br></div><div>To tackle the challenge of efficient simulation of irregular structures, in the last part of the thesis, we develop a method for the stability analysis of unsymmetrical numerical systems in time domain. An unsymmetrical system is traditionally avoided in numerical formulation since a traditional explicit simulation is absolutely unstable, and how to control the stability is unknown. However, an unsymmetrical system is frequently encountered in modeling and simulating of unstructured meshes and nonreciprocal electromagnetic and circuit devices. In our method, we reduce stability analysis of a large system into the analysis of dissembled single element, therefore provides a feasible way to control the stability of large-scale systems regardless of whether the system is symmetrical or unsymmetrical. We then apply the proposed method to prove and control the stability of an unsymmetrical matrix-free method that solves Maxwell’s equations in general unstructured meshes while not requiring a matrix solution.<br></div><div><br></div>

<p dir="ltr">This work introduces an innovative algorithm for co-simulating time-dependent Drift Diffusion (DD) equations with Maxwell\textquotesingle s equations to characterize semiconductor devices. Traditionally, the DD equations, derived from the Boltzmann transport equations, are used alongside Poisson\textquotesingle s equation to model electronic carriers in semiconductors. While DD equations coupled with Poisson\textquotesingle s equation underpin commercial TCAD software for micron-scale device simulation, they are limited by electrostatic assumptions and fail to capture time dependent high-frequency effects. Maxwell\textquotesingle s equations are fundamental to classical electrodynamics, enabling the prediction of electrical performance across frequency range crucial to advanced device fabrication and design. However, their integration with DD equations has not been studied thoroughly. The proposed method advances current simulation techniques by introducing a new broadband patch-based method to solve time-domain 3-D Maxwell\textquotesingle s equations and integrating it with the solution of DD equations. This technique is free of the low-frequency breakdown issues prevalent in conventional full-wave simulations. Meanwhile, it enables large-scale simulations with reduced computational complexity. This work extends the simulation to encompass the complete device, including metal contacts and interconnects. Thus, it captures the entire electromagnetic behavior, which is especially critical in electrically larger systems and high-frequency scenarios. The electromagnetic interactions of the device with its contacts and interconnects are investigated, providing insights into performance at the chip level. Validation through numerical experiments and comparison with results from commercial TCAD tools confirm the effectiveness of the proposed method. </p>

Dealing with the electromagnetic issue might bring a sort of discontinuous and nondifferentiable regions. Thus, it is of great interest to implement an appropriate optimisation approach, which can preserve the computational resources and come up with a global optimum. While not being trapped in local optima, as well as the feasibility to overcome some other matters such as nonlinear and phenomena of discontinuous with a large number of variables. Problems such as lengthy computation time, constraints put forward for antenna requirements and demand for large computer memory, are very common in the analysis due to the increased interests in tackling high-scale, more complex and higher-dimensional problems. On the other side, demands for even more accurate results always expand constantly. In the context of this statement, it is very important to find out how the recently developed optimization roles can contribute to the solution of the aforementioned problems. Thereafter, the key goals of this work are to model, study and design low profile antennas for wireless and mobile communications applications using optimization process over a computational electromagnetics numerical solution. The numerical solution method could be performed over one or hybrid methods subjective to the design antenna requirements and its environment. Firstly, the thesis presents the design and modelling concept of small uni-planer Ultra- Wideband antenna. The fitness functions and the geometrical antenna elements required for such design are considered. Two antennas are designed, implemented and measured. The computed and measured outcomes are found in reasonable agreement. Secondly, the work is also addressed on how the resonance modes of microstrip patches could be performed using the method of Moments. Results have been shown on how the modes could be adjusted using MoM. Finally, the design implications of balanced structure for mobile handsets covering LTE standards 698-748 MHz and 2500-2690 MHz are explored through using firefly algorithm method. The optimised balanced antenna exhibits reasonable matching performance including near-omnidirectional radiations over the dual desirable operating bands with reduced EMF, which leads to a great immunity improvement towards the hand-held. / General Secretariat of Education and Scientific Research Libya

The main objective of this research is to model and analyse complex electromagnetic problems by means of a new hybridised computational technique combining the frequency domain Method of Moments (MoM), Finite-Difference Time-Domain (FDTD) method and a subgridded Finite-Difference Time-Domain (SGFDTD) method. This facilitates a significant advance in the ability to predict electromagnetic absorption in inhomogeneous, anisotropic and lossy dielectric materials irradiated by geometrically intricate sources. The Method of Moments modelling employed a two-dimensional electric surface patch integral formulation solved by independent linear basis function methods in the circumferential and axial directions of the antenna wires. A similar orthogonal basis function is used on the end surface and appropriate attachments with the wire surface are employed to satisfy the requirements of current continuity. The surface current distributions on structures which may include closely spaced parallel wires, such as dipoles, loops and helical antennas are computed. The results are found to be stable and showed good agreement with less comprehensive earlier work by others. The work also investigated the interaction between overhead high voltage transmission lines and underground utility pipelines using the FDTD technique for the whole structure, combined with a subgridding method at points of interest, particularly the pipeline. The induced fields above the pipeline are investigated and analysed. FDTD is based on the solution of Maxwell¿s equations in differential form. It is very useful for modelling complex, inhomogeneous structures. Problems arise when open-region geometries are modelled. However, the Perfectly Matched Layer (PML) concept has been employed to circumvent this difficulty. The establishment of edge elements has greatly improved the performance of this method and the computational burden due to huge numbers of time steps, in the order of tens of millions, has been eased to tens of thousands by employing quasi-static methods. This thesis also illustrates the principle of the equivalent surface boundary employed close to the antenna for MoM-FDTD-SGFDTD hybridisation. It depicts the advantage of using hybrid techniques due to their ability to analyse a system of multiple discrete regions by employing the principle of equivalent sources to excite the coupling surfaces. The method has been applied for modelling human body interaction with a short range RFID antenna to investigate and analyse the near field and far field radiation pattern for which the cumulative distribution function of antenna radiation efficiency is presented. The field distributions of the simulated structures show reasonable and stable results at 900 MHz. This method facilitates deeper investigation of the phenomena in the interaction between electromagnetic fields and human tissues. / Ministry of Higher Education Malaysia and Universiti Tun Hussein Onn Malaysia (UTHM)

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[pt] Este trabalho apresenta uma abordagem inovadora para calcular autopares de operadores diferenciais (OD), utilizando programação genética (PG) e computação simbólica. Na literatura atual, o Método dos Elementos Finitos (MEF) e o Método das Diferenças Finitas (MDF) são os mais utilizados. Tais métodos usam discretização para converter o OD em uma matriz finita e, por isso, apresentam limitações como perda de acurácia e presença de soluções espúrias. Além disso, se o domínio do OD fosse alterado, os autopares precisariam ser calculados novamente, pois a representação matricial do operador depende dos parâmetros do problema. Nesse contexto, este trabalho propõe evoluir autofunções analiticamente usando PG, sem discretização do domínio. Com isso, é possível incorporar parâmetros, o que torna a solução obtida válida para uma classe de problemas. Este texto descreve o modelo para OD normais, aplicando conceitos de indivíduos multi-árvore e diferenciação simbólica. O modelo evolui auto-funções e, a partir delas, calcula os autovalores empregando a razão de Rayleigh. Experimentos baseados em aplicações da Física mostram que a técnica proposta é capaz de encontrar as autofunções analíticas com a acurácia igual ou melhor que as técnicas numéricas supracitadas. Finalmente, a técnica proposta é aplicada ao problema de propagação de ondas eletromagnéticas em poços de petróleo em ULF e UHF. As soluções analíticas são dadas em função do diâmetro e do percentual de incrustações no poço. Os resultados mostram que, para um conjunto suficientemente grande de valores distintos dos parâmetros, a técnica apresenta tempo de execução inferior às técnicas clássicas, mantendo a acurácia destas. / [en] This work presents an innovative approach to calculate the eigenpairs of linear differential operators (LDO), employing genetic programming (GP) and symbolic computation. In the current literature, the Finite Element Method (FEM) and the Finite Difference Method (FDM) are more commonly used. Such methods use discretization to convert the LDO to a finite matrix, therefore causing loss of accuracy and presence of spurious solutions. Additionally, if the domain of the LDO was changed, the eigenpairs would need to be recalculated, since the matrix representation of the LDO depends on the parameters of the problem. In this context, this work proposes to evolve eigenfunctions analytically using GP, without domain discretization. Hence, it is possible to incorporate the parameter, which makes a obtained solution valid for a class of problems. This text describes the model for normal LDO, applying concepts of multi-tree individuals and symbolic differentiation. The presented model evolves eigenfunctions and, then, calculates the eigenvalues using the Rayleigh quotient. Experiments based on Physics problems show that the proposed technique is able to find the analytical eigenfunctions with the same accuracy of the numerical techniques mentioned above. Finally, the proposed technique is applied to the problem of propagation of electromagnetic waves in oil wells in ULF and UHF. The analytical solutions are given as a function of the diameter and percentage of CaCO in the well. The results show that, for a sufficiently large set of distinct values of the parameters, the technique presents execution time inferior to the FEM, while maintaining its accuracy.