We study two finite element methods for solving time-harmonic electromagnetic and acoustic problems: the discontinuous Petrov-Galerkin (DPG) method and the hybrid discontinuous Galerkin (HDG) method. The DPG method for the Helmholtz equation is studied using a test space normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. We find that, as the parameter approaches zero, better results are obtained, under some circumstances. A dispersion analysis on the multiple interacting stencils that form the DPG method shows that the discrete wavenumbers of the method are complex, explaining the numerically observed artificial dissipation in the computed wave approximations. Since the DPG method is a nonstandard least-squares Galerkin method, its performance is compared with a standard least-squares method having a similar stencil. We study the HDG method for complex wavenumber cases and show how the HDG stabilization parameter must be chosen in relation to the wavenumber. We show that the commonly chosen HDG stabilization parameter values can give rise to singular systems for some complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. For real wavenumbers, results from a dispersion analysis for the Helmholtz case are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method shows that its wavenumber errors are an order smaller than those of the HDG method. We conclude by presenting some contributions to the development of software tools for using the DPG method and their application to a terahertz photonic structure. We attempt to simulate field enhancements recently observed in a novel arrangement of annular nanogaps.

A finite element tool has been developed to design and investigate a multi-hull composite ship structure, and a hybrid hull of identical length and beam. Hybrid hull structure is assembled by Titanium alloy (Ti-6Al-4V) frame and sandwich composite panels. Wave loads and slamming loads acting on both hull structures have been calculated according to ABS rules at sea state 5 with a ship velocity of 40 knots. Comparisons of deformations and stresses between two sets of loadings demonstrate that slamming loads have more detrimental effects on ship structure. Deformation under slamming is almost one order higher than that caused by wave loads. Also, Titanium frame in hybrid hull significantly reduces both deformation and stresses when compared to composite hull due to enhancement of in plane strength and stiffness of the hull. A 73m long hybrid hull has also been investigated under wave and slamming loads in time domain for dynamic analysis. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2013.

Thesis. 1978. M.C.P.--Massachusetts Institute of Technology. Dept. of Urban Studies and Planning. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ROTCH. / Includes bibliographical references. / M.C.P.

First, we investigate the steady Euler flows through a general 3-D axially symmetric infinitely long nozzles without irrotationality. Global existence and uniqueness of subsonic solution are established, when the variation of Bernoulli's function in the upstream is sufficiently small and mass flux has an upper critical value. / Second, we concerns the following transonic shock phenomena in a class of de Laval nozzles with porous medium posed by Courant-Friedrichs: Given a appropriately large receiver pressure pr, if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes pr. We investigate this problem for the full Euler equations, the stability of the transonic shock is proved when the upstream supersonic flow is a small steady perturbation of the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation. / Duan, Ben. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 125-137). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Weng, Shangkun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 73-78). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Existence and Uniqueness results of transonic shock solution to full Euler system in a large variable nozzle --- p.11 / Chapter 2.1 --- The mathematical description of the transonic shock problem and main results --- p.11 / Chapter 2.2 --- The reformulation on problem (2.1.1) with (2.1.5)-(2.1.9) --- p.18 / Chapter 2.3 --- An Iteration Scheme --- p.30 / Chapter 2.4 --- A priori estimates and proofs of Theorem 2.2.1 and Theorem 2.1.1 --- p.39 / Chapter 3 --- A monotonic theorem on the shock position with respect to the exit pressure --- p.50 / Chapter 4 --- Discussions and Future work --- p.64 / Chapter 5 --- Appendix --- p.66 / Chapter 5.1 --- Appendix A: Background solution --- p.66 / Chapter 5.2 --- Appendix B: An outline of the proof of Theorem 2.1.2 --- p.67

This thesis deals with the topic of reflection and refraction of light from the boundary of nonlinear materials in general, and saturating amplifiers in particular. We first study some of the basic properties of the light waves in nonlinear materials. We then develop a general formalism to model the reflection and refraction of light with an arbitrary angle of incidence from the boundary of a nonlinear medium. This general formalism is then applied to the case of reflection and refraction from the boundary of linear dielectrics. It will be shown that in this limit, it reduces to the well known Fresnel and Snell's formulas. We also study the interface of a saturating amplifier. The wave equation we use for this purpose is approximate, in the sense that it assumes the amplitude of the wave does not vary significantly in a distance of a wave length. The limits and implications of this approximation are also investigated. We derive expressions for electric field and intensity reflection and transmission coefficients for such materials. In doing so, we make sure that the above mentioned approximation is not violated. These results are compared with the case of reflection and refraction from the interface of a linear dielectric.

A global, multi-level, wave-mean flow model based on an approximate version of the primitive equations is developed to investigate the development of a baroclinic wave field initially confined to a single zonal wavenumber. The effects of physical processes (surface drag and thermal damping) and internal diffusion on the evolution have been examined. The nature of the mean flow adjustment by the nonlinear baroclinic waves is also studied. For a simulation with a relatively strong internal diffusion it is found that a single life cycle characterized by baroclinic growth and barotropic decay is obtained (as in Simmons and Hoskins, 1978), whereas with weaker diffusion the wave undergoes secondary life cycles before a nearly wave-free state is reached (as in Barnes and Young, 1991). In an experiment with weak 4th order diffusion secondary life cycles occur with little net decay. Relatively strong barotropic growth follows the initial life cycle. In experiments with surface drag (Rayleigh friction) and thermal damping (Newtonian cooling), repeated life cycles of baroclinic growth and barotropic decay can be obtained. It is found that in the complete absence of surface drag, the flow evolves to a nearly wave-free state after one secondary cycle. This demonstrates that surface drag plays an important role in nonlinear baroclinic instability. With relatively strong surface drag multiple life cycle behavior is found for sufficiently strong thermal damping. Such a behavior strengthens for very strong thermal damping. A steady wave state in which the wave amplitude equilibrates at an essentially constant level has only been obtained with very strong "potential vorticity damping". Both the "barotropic governor" process (James and Gray, 1986) and the baroclinic adjusment process are responsible for major parts of the stabilization of the mean flow in simulations with and without surface drag and thermal damping. However, the "barotropic governor" process dominates the flow evolution in the model simulations without surface drag and thermal damping. The "barotropic governor" modifies the meridional gradient of zonal mean potential vorticity, which influences the baroclinic adjustment. / Graduation date: 1992

A technique that allows for nonparallel interfaces and lateral inhomogeneities in an irregular layered medium is described. The formulation combines a semidiscrete finite-element technique with a perturbation method, providing an approximate treatment of wave propagation in irregular layered media. The procedure treats the irregularities as perturbations with respect to a reference, horizontally-layered, laterally-homogeneous medium and produces approximations of the perturbed wave motion with little additional computation effort. Within the framework of the method, consistent transmitting boundaries and other semidiscrete hyperelements as well as Green’s functions, already available for regular layered media, can be reformulated. The method is relevant in problems of foundation dynamics, ground response to seismic waves and site characterization. Example problems are presented toward evaluation of the effectiveness of the method. / text

The interaction of steep waves with structures is a complex problem which is still not fully understood, and is of great importance for the design of offshore structures. A particular problem of interest is the phenomenon of ringing which is highly nonlinear. In this thesis a number of inviscid free surface flow problems are simulated using a finite element model. The free surface boundary condition is fully nonlinear, meaning nonlinear effects up to very high order can be simulated, depending on mesh resolution. The model uses a fully automatic unstructured mesh generator; this allows the mesh to change its shape and structure as the free surface deforms. Two unstructured mesh generators have been developed, one based on the advancing front method, the other on the Voronoi technique. Variations of each method are examined. Both methods give good quality meshes. The advancing front technique is found to be faster, but the Voronoi method is more robust and reliable. In addition to the standard finite element method, a sigma transformed version of the finite element formulation has been developed as an alternative. Both techniques have been used for the numerical simulations. The sigma transformation involves stretching of the mesh between the bed and free surface, and so has the advantage that remeshing is avoided. The standard finite element method is straightforward to apply to problems involving submerged arbitrary shaped bodies. Simulations have been performed of a number of test cases, such as a standing wave of large amplitude, a base excited tank and steep travelling waves. Convergence tests were carried out and results found to be in close agreement with analytical and alternative numerical solutions of Wu and Eatock Taylor (1994), Wu et al. (1998) and Chern et al. (1999). The force on a submerged horizontal cylinder due a travelling wave has been calculated. First and second order components have been obtained by Fourier analysis. The results have been compared with the theoretical predictions of Ogilvie (1963), Vada (1987) and Wu and Eatock Taylor (1990) and the experimental results of Chaplin (1984).

Using a two-dimensional nonlinear numerical simulation of a (viscous) stratified shear layer, strong instabilities resulted from the resonant interaction of a long linearly neutrally stable wave and the corresponding fastest growing wave. This linearly fastest growing wave, with optimal initial conditions, grows initially at a rate five times that predicted by linear theory. With other initial conditions, the linearly fastest growing wave may actually decay. The possibility of this type of interaction is suggested by the weakly nonlinear theory (cf. Maslowe, 1977). This coupled system of fourth order nonl inear partial differential equations was solved using a modified pseudospectral scheme for the spatial variables, incorporating the use of fast Fourier transforms to calculate spatial derivatives, and a second order Adams-Bashforth scheme for the temporal derivatives . / Dans cette etude, en utilisant une simulation numerique nonlineaire a deux dimensions d'une couche stratifiee, decollee et visqueuse, on obtint des resultats interessants a partir des cas correspondant a l'interaction resonnante d'une onde longue a stabilite neutre et d'une onde courte qui croit la plus rapidement selon la theorie lineaire. En utilisant certaines conditions initiales, l'onde courte croit initialement a un taux cinq fois superieur a celui predit par la theorie lineaire. Avec d'autres conditions initiales l'onde courte decroit. La possibilite de ce genre d'interaction est predite par la theorie faiblement nonlineaire (voir Maslowe, 1977). Ce systeme couple aux equations nonlineaires du quatrieme ordre aux derivees partielles, est resolu par une methode pseudo-spectrale modifiee, pour les variables spatiales, et une methode Adams-Bashforth du second ordre pour les derivees temporelles. fr