<p dir="ltr">As the design of computer chips heavily relies on computer simulations, it is envisioned that numerical modeling will play an increasingly important role in the development of unconventional computing technologies. This thesis studies the computational frameworks related to the development of unconventional computing, including probabilistic computing and quantum computing. The capability of probabilistic computing in solving NP-complete number theory problems is demonstrated. Generalized Helmholtz decomposition is shown as a theoretical basis for quantization of electromagnetic fields via numerical mode decomposition. A 2D demonstration of numerical quantization with finite difference method is presented. A computational framework amenable to integral equation solver is proposed to investigate the scattering effect on momentum-entangled photons from spontaneous parametric downconversion. A generic model to investigate field-matter interaction with nonlinearity is presented.</p>

<p>In this study we propose a fast hybrid spectral-element time-domain (SETD) / finite-element time-domain (FETD) method for transient analysis of multiscale electromagnetic problems, where electrically fine structures with details much smaller than a typical wavelength and electrically coarse structures comparable to or larger than a typical wavelength coexist.</p><p>Simulations of multiscale electromagnetic problems, such as electromagnetic interference (EMI), electromagnetic compatibility (EMC), and electronic packaging, can be very challenging for conventional numerical methods. In terms of spatial discretization, conventional methods use a single mesh for the whole structure, thus a high discretization density required to capture the geometric characteristics of electrically fine structures will inevitably lead to a large number of wasted unknowns in the electrically coarse parts. This issue will become especially severe for orthogonal grids used by the popular finite-difference time-domain (FDTD) method. In terms of temporal integration, dense meshes in electrically fine domains will make the time step size extremely small for numerical methods with explicit time-stepping schemes. Implicit schemes can surpass stability criterion limited by the Courant-Friedrichs-Levy (CFL) condition. However, due to the large system matrices generated by conventional methods, it is almost impossible to employ implicit schemes to the whole structure for time-stepping.</p><p>To address these challenges, we propose an efficient hybrid SETD/FETD method for transient electromagnetic simulations by taking advantages of the strengths of these two methods while avoiding their weaknesses in multiscale problems. More specifically, a multiscale structure is divided into several subdomains based on the electrical size of each part, and a hybrid spectral-element / finite-element scheme is proposed for spatial discretization. The hexahedron-based spectral elements with higher interpolation degrees are efficient in modeling electrically coarse structures, and the tetrahedron-based finite elements with lower interpolation degrees are flexible in discretizing electrically fine structures with complex shapes. A non-spurious finite element method (FEM) as well as a non-spurious spectral element method (SEM) is proposed to make the hybrid SEM/FEM discretization work. For time integration we employ hybrid implicit / explicit (IMEX) time-stepping schemes, where explicit schemes are used for electrically coarse subdomains discretized by coarse spectral element meshes, and implicit schemes are used to overcome the CFL limit for electrically fine subdomains discretized by dense finite element meshes. Numerical examples show that the proposed hybrid SETD/FETD method is free of spurious modes, is flexible in discretizing sophisticated structure, and is more efficient than conventional methods for multiscale electromagnetic simulations.</p> / Dissertation

La connaissance précise des champs électromagnétiques rayonnés par les dispositifs hyperfréquences nécessite des outils instrumentaux permettant la mesure directe ou indirecte de ces champs. La technique du scan champ proche fait partie de ces outils. Ce manuscrit décrit les travaux de caractérisation des sondes électromagnétiques pour une plate-forme de scan champ proche développée au laboratoire LAPLACE. L’accent a été mis sur la simulation électromagnétique des dispositifs de test utilisés dans le travail de déconvolution du facteur d’antenne des sondes de champs magnétiques ou électriques. Ces dispositifs comprennent aussi bien des structures planaires telles que des interconnexions en ligne microruban que des composants en guide d’ondes tels que des guides ouverts de formes rectangulaire ou circulaire. Pour analyser ces structures des logiciels commerciaux basés sur la méthode des différences finis ont été utilisés. Dans le cas des structures rayonnantes un programme basé sur la méthode de l’opérateur transverse a été développé, permettant la détermination de l’admittance de rayonnement et les champs rayonnés en zones proche et lointaine. Les résultats obtenus ont été validés par des simulations avec des outils commerciaux, et par des mesures réalisés au laboratoire. / The accurate knowledge of electromagnetic fields radiated by microwave devices requires instrumental tools for direct or indirect measurement of these fields. Near-field scan technique is one of those tools. This manuscript describes the work done to characterize electromagnetic probes using a near field scan platform developed in the laboratory LAPLACE. We focused our work on the electromagnetic simulation of test devices that are used in the deconvolution of antenna factor of magnetic or electric probes. These devices include both planar structures such as microstrip line and also waveguide components such as rectangular or circular open-ended waveguides. To analyze these structures, commercial software based on finite element method was used. In case of radiating structures, a program based on transverse operator method was developed. It allows the determination of the admittance of radiation and the radiated electromagnetic fields in near-field and far-field regions. The results were validated by simulations with commercial tools, and measurements made in the laboratory.

Computer simulation of electromagnetic behaviour of a device is a common practice in modern engineering. Maxwell's equations are solved on a computer with help of numerical methods. Contemporary devices constantly grow in size and complexity. Therefore, new numerical methods should be highly efficient. Many industrial and research applications of numerical methods need to account for the frequency dependent materials. The Finite-Difference Time-Domain (FDTD) method is one of the most widely adopted algorithms for the numerical solution of Maxwell's equations. A major drawback of the FDTD method is the interdependence of the spatial and temporal discretisation steps, known as the Courant-Friedrichs-Lewy (CFL) stability criterion. Due to the CFL condition the simulation of a large object with delicate geometry will require a high spatio-temporal resolution everywhere in the FDTD grid. Application of subgridding increases the efficiency of the FDTD method. Subgridding decomposes the simulation domain into several subdomains with different spatio-temporal resolutions. The research project described in this dissertation uses the Huygens Subgridding (HSG) method. The frequency dependence is included with the Auxiliary Differential Equation (ADE) approach based on the one-pole Debye relaxation model. The main contributions of this work are (i) extension of the one-dimensional (1D) frequency-dependent HSG method to three dimensions (3D), (ii) implementation of the frequency-dependent HSG method, termed the dispersive HSG, in Fortran 90, (iii) implementation of the radio environment setting from the PGM-files, (iv) simulation of the electromagnetic wave propagating from the defibrillator through the human torso and (v) analysis of the computational requirements of the dispersive HSG program.

Many systems designed by electrical & computer engineers rely on electromagnetic (EM) signals to transmit, receive, and extract either information or energy. In many cases, these systems are large and complex. Their accurate, cost-effective design requires high-fidelity computer modeling of the underlying EM field/material interaction problem in order to find a design with acceptable system performance. This modeling is accomplished by projecting the governing Maxwell equations onto finite dimensional subspaces, which results in a large matrix equation representation (Zx = b) of the EM problem. In the case of integral equation-based formulations of EM problems, the M-by-N system matrix, Z, is generally dense. For this reason, when treating large problems, it is necessary to use compression methods to store and manipulate Z. One such sparse representation is provided by so-called H^2 matrices. At low-to-moderate frequencies, H^2 matrices provide a controllably accurate data-sparse representation of Z. The scale at which problems in EM are considered ``large'' is continuously being redefined to be larger. This growth of problem scale is not only happening in EM, but respectively across all other sub-fields of computational science as well. The pursuit of increasingly large problems is unwavering in all these sub-fields, and this drive has long outpaced the rate of advancements in processing and storage capabilities in computing. This has caused computational science communities to now face the computational limitations of standard linear algebraic methods that have been relied upon for decades to run quickly and efficiently on modern computing hardware. This common set of algorithms can only produce reliable results quickly and efficiently for small to mid-sized matrices that fit into the memory of the host computer. Therefore, the drive to pursue larger problems has even began to outpace the reasonable capabilities of these common numerical algorithms; the deterministic numerical linear algebra algorithms that have gotten matrix computation this far have proven to be inadequate for many problems of current interest. This has computational science communities focusing on improvements in their mathematical and software approaches in order to push further advancement. Randomized numerical linear algebra (RandNLA) is an emerging area that both academia and industry believe to be strong candidates to assist in overcoming the limitations faced when solving massive and computationally expensive problems. This thesis presents results of recent work that uses a random sampling method (RSM) to implement algebraic operations involving multiple H^2 matrices. Significantly, this work is done in a manner that is non-invasive to an existing H^2 code base for filling and factoring H^2 matrices. The work presented thus expands the existing code's capabilities with minimal impact on existing (and well-tested) applications. In addition to this work with randomized H^2 algebra, improvements in sparse factorization methods for the compressed H^2 data structure will also be presented. The reported developments in filling and factoring H^2 data structures assist in, and allow for, the further pursuit of large and complex problems in computational EM (CEM) within simulation code bases that utilize the H^2 data structure.

No description available.

No description available.

No description available.

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.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this work the Method of Manufactured Solutions (MMS) is introduced for the code veri cation of full-wave frequency dependent electromagnetic computational software. At rst the method is sketched in the context of the veri cation and validation process and the need for proper code veri cation is highlighted. Subsequently, the MMS is investigated in its natural context: the Finite Element Method, speci cally for the E- eld Vector Wave Equation. The usefulness of the method to detect error in a computational code is demonstrated. The selection of Manufactured Solutions is discussed and it is demonstrated how it can be used to nd the probable cause of bugs. Mutation testing is introduced and used to show the ability to detect errors present in code. The MMS is nally applied in a novel manner to a Method of Moments (MoM) code. The challenges of numerical integration associated with the application of the operator is discussed and correct integration is successfully demonstrated. Subsequently the MMS is demonstrated to be successfully applied to the MoM and mutation testing is used to demonstrate the practical e cacy of the method. The application of the MMS to the MoM is the main contribution of this work. / AFRIKAANSE OPSOMMING: Die Metode van Vervaardigde Oplossings (MVO) word hier bekend gestel vir die veri kasie van numeriese volgolf frekwensie-afhanklike elektromagnetise kode. Die metode word eerstens in die bre e konteks van algemene veri kasie en validasie geplaas en gevolglik word die noodsaaklikheid van kode veri kasie beklemtoon. Daarna, word die toets-metode in die konteks van die Eindige Element Metode vir die E-veld vektorgolf vergelyking bestudeer. Die MVO is oorspronklik ontwikkel in die di erentiaalvergelyking omgewing. Die bruikbaarheid van die metode vir elektromagnetiese simulasies word prakties gedemonstreer deur die opsporing van werklike foute. Die metode word ook verder ondersoek vir die oorsprong van foute. Mutasietoetsing word bekendgestel en word gebruik om die metode verder prakties te veri eer. Die MVO word laastens in 'n nuwe manier gebruik om 'n Moment Metode kode te veri eer. Die praktiese probleme betrokke by numeriese integrasie word ondersoek en die korrekte toepassing van die integraal operator word prakties gedemonstreer. Daarna, word die MVO in hierdie konteks gedemonstreer deur verskeie voorbeelde te ondersoek. Mutasietoetsing word weereens gebruik om na die e ektiewiteit van die MVO te kyk om 'n Moment Metode kode te toets. Die toepassing van die MVO op 'n Moment Metode kode is die hoof bydrae van hierdie werk.