<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

The interaction between thermal convection and magnetic field is of interest in geophysical and astrophysical problems as well as in metallurgical processes such as casting or crystallization. A magnetic field may act in such a way to damp the convective velocity field in the melt or to reorganize the flow aligned with the magnetic field. This ability to manipulate the flow field is of technological importance in industrial processes. In this work, a direct numerical simulation of three-dimensional Boussinesq convection in a horizontal layer of electrically conducting fluid confined between two perfectly conducting horizontal plates heated from below in a gravitational and magnetic field is performed using a spectral element method. Periodic boundary conditions are assumed in the horizontal directions. The numerical model is then used to study the effects of imposing magnetic field. Finally, a low dimensional representation scheme is presented based on the Karhunen-Loeve approach.

Supercritical fluid extraction has been used to recover biomaterials from natural matrices. Mathematical modeling of the extraction is required for process design and scale up. Existing models in literature are correlative and dependent upon the experimental data. Construction of predictive models giving reliable results in the lack of experimental data is precious. The long term objective of this study was to construct a predictive mass transfer model, representing supercritical fluid extraction of biomaterials in packed beds by the method of volume averaging. In order to develop mass transfer equations in terms of volume averaged variables, velocity and velocity deviation fields, closure variables were solved for a specific case and the coefficients of volume averaged mass transfer equation for the specific case were computed using one and two-dimensional geometries via analytical and numerical solutions, respectively. Spectral Element method with Domain Decomposition technique, Preconditioned Conjugate Gradient algorithm and Uzawa method were used for the numerical solution. The coefficients of convective term with additional terms of volume averaged mass transfer equation were similar to superficial velocity. The coefficients of dispersion term were close to diffusivity of oil in supercritical carbon dioxide. The coefficients of interphase mass transfer term were overestimated in both geometries. Modifications in boundary conditions, change in geometry of particles and use of three-dimensional computations would improve the value of the coefficient of interphase mass transfer term.

<p>Numerical methods such as Monte Carlo method (MCM), finite difference method (FDM) and finite element method (FEM) have been successfully implemented to solve financial partial differential equations (PDEs). Sophisticated computational algorithms are strongly desired to further improve accuracy and efficiency.</p><p>The relatively new spectral element method (SEM) combines the exponential convergence of spectral method and the geometric flexibility of FEM. This dissertation carefully investigates SEM on the pricing of European options and their Greeks (Delta, Gamma and Theta). The essential techniques, Gauss quadrature rules, are thoroughly discussed and developed. The spectral element method and its error analysis are briefly introduced first and expanded in details afterwards.</p><p>Multi-element spectral element method (ME-SEM) for the Black-Scholes PDE is derived on European put options with and without dividend and on a condor option with a more complicated payoff. Under the same Crank-Nicolson approach for the time integration, the SEM shows significant accuracy increase and time cost reduction over the FDM. A novel discontinuous payoff spectral element method (DP-SEM) is invented and numerically validated on a European binary put option. The SEM is also applied to the constant elasticity of variance (CEV) model and verified with the MCM and the valuation formula. The Stochastic Alpha Beta Rho (SABR) model is solved with multi-dimensional spectral element method (MD-SEM) on a European put option. Error convergence for option prices and Greeks with respect to the number of grid points and the time step is analyzed and illustrated.</p> / Dissertation

A Direct Numerical Simulation of an iced Natural Laminar Flow NLF-0414 airfoil is carried out using a high-order spectral element method for low chord Reynolds numbers (O(10^5)). This study aims to advance the state-of-the-art for accurate computational modeling of transition, iced airfoil aerodynamics, and irregular surface spectral element method Direct Numerical Simulation. Ice accretion over an aircraft, ranging from light to severe, changes the aerodynamic profile of the airfoil and alters the overall performance. The literature presents simulations that have been carried out with a range of turbulence models which fail to accurately capture the complex physics of these flows. The iced profiles being studied, Run 606 and 622-2D, were obtained from a Technical Publication by NASA on iced airfoils including the NLF-0414, and were selected as they are relatively lightly iced profiles of the NLF-0414. The largest bottleneck with the current advancement in High Performance Computing is the computation time required for Direct Numerical Simulation. Results such as lift, drag, pressure, and skin friction coefficients, for a clean NLF-0414 and two lightly iced NLF-0414 airfoils at chord Reynolds numbers of Rec = 1 x 10^5 and Rec = 2 x 10^5 are visualized and discussed, showing the degradation of the natural laminar flow due to ice accretion. Turbulence statistics are calculated to study the effective contributions of turbulent fluctuations in the flow to further understand the flow physics near transition. The detailed study of these six cases has led us to 1) further understand the complexities of the transition process on iced airfoils, 2) observe and explain the sometimes unexpected changes in aerodynamic performance due to varying iced geometries, and 3) establish a methodology for spectral element method Direct Numerical Simulations.

In recent years, the desperate need for reliable clean and relatively small power demand has emerged for edge-of-grid or off-grid regions to keep pace with development demands. A salient technology that has gained much attention for this purpose is the Small Modular Reactors, i.e., SMRs. SMRs differ from conventional Nuclear Power Plants (NPPs) in many aspects, specifically the enclosing structure of the reactor. The burial depth of the SMR structure is expected to reach great depths. For example, the substructure depth reaches 30 m in the SMR design proposed by NuScale (NuScale Power, 2020). Consequently, seismic analysis of deeply embedded structures with a relatively small footprint has been identified as one of the challenges to the safe implementation of SMR technology (DIS-16-04, 2016). Such structures are expected to be more sensitive to surface wave propagation and the seismic interaction with nearby substructures and nonstructural elements such as pipelines. This dissertation develops analytical and numerical methods to analyze the seismic earth pressure exerted on the SMR substructure by considering the effects of seismic surface waves, structure-soil-structure interaction (SSSI), and the interaction with nearby pipelines. The three-dimensional wave propagation theory is employed in the analysis. Solutions for the earth pressure induced by Rayleigh waves are obtained for substructures deeply embedded into homogeneous or multilayered soil profiles. In addition, the effect of thin soil layer (stiff or soft) soils in a soil profile is investigated in the presence of Rayleigh waves. Furthermore, additional earth pressure due to SSSI is examined, and a simplified procedure is proposed based on the three-dimensional wave propagation theory and a guided flow chart to track seismic wave interference. The SSSI analysis yields solutions for the optimal distance between substructures corresponding to the minimum SSSI in new designs. The interaction between substructures and nearby pipelines is explored numerically using the Spectral Element Method. SPECFEM2D software is adopted to perform the analysis, where the three-dimensional wave propagation is successfully implemented. Based on the analysis for pipelines with different configurations, general conclusions are drawn regarding the additional earth pressure on substructures and pipelines based on a comprehensive parametric study of various parameters. In addition, this research also provides an approach to determine the backfill configuration and the selection of backfill materials, which could minimize the seismic amplitudes transmitted to substructures. / Thesis / Doctor of Philosophy (PhD) / Small Modular Reactors (SMRs) are the cornerstone of recent developments in the nuclear industry. However, the SMRs technology faces several safety-related challenges, which includes the earthquake hazards related to the large embedment depth of the enclosing structure. In particular, the major concerns are about the risks related to seismic surface waves as well as the seismic interaction between nearby structural and non-structural elements (e.g., pipelines). The thesis addressed these major concerns by developing analytical and numerical methods to complement the analysis for the integrity of SMRs with sufficient seismic resistance. The solutions are verified and benchmarked using data in the literature. Future researches are suggested to further improve seismic analysis of SMRs.

Unbounded domains often appear in engineering applications, such as acoustic or elastic wave radiation from a body immersed in an infinite medium. To simulate the unboundedness of the domain special boundary conditions have to be imposed: the Sommerfeld radiation condition. In the present work we focused on steady-state wave propagation. The objective of this research is to obtain accurate prediction of phenomena occurring in exterior acoustics and elastodynamics and ensure the quality of the solutions even for high wavenumbers. To achieve this aim, we develop higher-order domain-based schemes: Spectral Element Method (SEM) coupled to Dirichlet-to-Neumann (DtN ), Perfectly Matched Layer (PML) and Infinite Element (IEM) methods. Spectral elements combine the rapid convergence rates of spectral methods with the geometric flexibility of the classical finite element methods. The interpolation is based on Chebyshev and Legendre polynomials. This work presents an implementation of these techniques and their validation exploiting some benchmark problems. A detailed comparison between the DtN, PML and IEM is made in terms of accuracy and convergence, conditioning and computational cost.

The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular nodal distributions, namely Lobatto distribution and Fekete distribution, are compared in terms of accuracy and implementation complexity. Accuracies provided by triangular and quadrilateral grids of equal computational size are compared. Adaptive mesh refinement studies are conducted using three different error indicators, including a novel one based on elemental mass loss. Effect of modifying the least-squares functional by multiplying the continuity equation by a weight factor is investigated in regards to mass conservation.

Die Dissertation behandelt methodische und algorithmische Aspekte der Spektralelementemethode zur räumlichen Diskretisierung partieller Differentialgleichungen. Die Weiterentwicklung einer symmetriebasierten Faktorisierung ermöglicht effiziente Operatoren für Tetraederelemente. Auf Grundlage einer umfassenden Leistungsanalyse werden Engpässe in der Implementierung der Operatoren identifiziert und durch algorithmische Modifikationen der Methode eliminiert.

Submitted by Sanderson Manoel Da Conceição (enders83@yahoo.com.br) on 2018-08-24T00:09:53Z No. of bitstreams: 1 TeseDR_Sanderson.pdf: 5806318 bytes, checksum: 51410134afd7ae86d0783074d6012e88 (MD5) / Approved for entry into archive by Cristina Alexandra de Godoy null (cristina@adm.feis.unesp.br) on 2018-08-24T17:09:49Z (GMT) No. of bitstreams: 1 conceicao_sm_dr_ilha.pdf: 5957405 bytes, checksum: 16cab2d9c84f81cd3cd4ff0b9fa36219 (MD5) / Made available in DSpace on 2018-08-24T17:09:49Z (GMT). No. of bitstreams: 1 conceicao_sm_dr_ilha.pdf: 5957405 bytes, checksum: 16cab2d9c84f81cd3cd4ff0b9fa36219 (MD5) Previous issue date: 2016-12-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A ideia central deste trabalho é utilizar o método dos Elementos Espectrais (SEM, do inglês Spectral Element Method) para aplicações de controle ativo de vibrações e monitoramento da integridade estrutural (SHM, do inglês Structural Health Monitoring). Diversos trabalhos têm abordado estes tópicos de forma independente. No entanto, para aplicações reais de engenharia, utilizar os mesmos atuadores, sensores e sistemas de aquisição de dados para controle e monitoramento pode reduzir investimentos e simplificar processos. Por esta motivação, este trabalho apresenta um estudo de modelos espectrais para estruturas do tipo viga considerando aplicações de controle de vibrações e monitoramento da integridade estrutural. Na modelagem são considerados os modelos de vigas de Euler-Bernoulli e Timoshenko, além de transdutores piezelétricos acoplados. A técnica de controle clássico PID (Proporcional, Integral, Derivativo) é explorada e uma nova modelagem é proposta para se considerar técnicas modernas de controle por realimentação de estados na formulação espectral. Em particular, discute-se o controlador LQR (do inglês, Linear Quadratic Regulator), no entanto, a metodologia permite se considerar outras técnicas de controle por realimentação baseada na representação no espaço de estados. Também, especificamente para monitoramento estrutural, no presente trabalho de tese apresenta-se uma discussão sobre índices de detecção de danos. Índices de detecção calculados a partir de sinais experimentais têm sido amplamente utilizados em trabalhos da literatura de SHM. No entanto, pouco tem sido esclarecido sobre seus comportamentos em função das características estruturais e dos danos. Neste sentido, o presente trabalho apresenta uma discussão do comportamento de índices baseados na norma H2, norma H∞ e no CCDM (Correlation coefficient deviation metric), para duas faixas de frequência, em função da severidade do dano e quantidade de amortecimento no sistema. Os resultados obtidos indicam que a formulação por Elementos Espectrais é adequada para viabilizar os projetos simultâneos de um controlador de vibrações e um sistema de monitoramento estrutural utilizando os mesmos equipamentos e simplificando análises ao se utilizar um único modelo dinâmico do sistema. / The main idea of this thesis is to use the Spectral Element Method (SEM), in applications of Active Vibration Control (AVC) and Structural Health Monitoring (SHM). These two topics have been approached in several works, but in an independent way. However, for real engineering applications, to use the same actuators, sensors and data acquisition systems to active control and structural monitoring can reduce the costs and simplify processes. For this reason, this thesis presents a study of spectral models for beam-like structures considering applications of vibration control and structural health monitoring. The Euler-Bernoulli and Timoshenko beam theories are used in the spectral modelling and the piezelectric transducers bonded in the structures are also considered. A classical control technique, PID (Proportional, Integral, Derivative) is explored and a new modelling approach to consider modern control methods of state feedback is proposed in spectral formulation. In particular, the Linear Quadratic Regulator (LQR) is discussed, however, this methodology allows for any other state feedback control techniques based in state space representation. Also, specifically for structural monitoring, is presented a discussion about damage detection indices. Detection indices computed from experimental data have been widely used in SHM studies. However, little has been clarified about their behaviours due to structural characteristics and damages. In this context, this work presents a discussion of the behaviour of indices based in the H2 norm, H∞ norm and CCDM (Correlation coefficient deviation metric), for two frequency ranges, depending on the severity of damage and amount of damping in the system. The obtained results indicate that the spectral element formulation is suited to enable the simultaneous design of a vibration controller and a structural monitoring system using the same data acquisition systems and simplifying analysis when using just one dynamic model of the system.