Fast and accurate solvers for capacitance extraction are needed by the VLSI industry in order to achieve good design quality in feasible time. With the development of technology, this demand is increasing dramatically. Three-dimensional capacitance extraction algorithms are desired due to their high accuracy. However, the present 3D algorithms are slow and thus their application is limited. In this dissertation, we present several novel techniques to significantly speed up capacitance extraction algorithms based on boundary element methods (BEM) and to compute the capacitance extraction in the presence of floating dummy conductors. We propose the PHiCap algorithm, which is based on a hierarchical refinement algorithm and the wavelet transform. Unlike traditional algorithms which result in dense linear systems, PHiCap converts the coefficient matrix in capacitance extraction problems to a sparse linear system. PHiCap solves the sparse linear system iteratively, with much faster convergence, using an efficient preconditioning technique. We also propose a variant of PHiCap in which the capacitances are solved for directly from a very small linear system. This small system is derived from the original large linear system by reordering the wavelet basis functions and computing an approximate LU factorization. We named the algorithm RedCap. To our knowledge, RedCap is the first capacitance extraction algorithm based on BEM that uses a direct method to solve a reduced linear system. In the presence of floating dummy conductors, the equivalent capacitances among regular conductors are required. For floating dummy conductors, the potential is unknown and the total charge is zero. We embed these requirements into the extraction linear system. Thus, the equivalent capacitance matrix is solved directly. The number of system solves needed is equal to the number of regular conductors. Based on a sensitivity analysis, we propose the selective coefficient enhancement method for increasing the accuracy of selected coupling or self-capacitances with only a small increase in the overall computation time. This method is desirable for applications, such as crosstalk and signal integrity analysis, where the coupling capacitances between some conductors needs high accuracy. We also propose the variable order multipole method which enhances the overall accuracy without raising the overall multipole expansion order. Finally, we apply the multigrid method to capacitance extraction to solve the linear system faster. We present experimental results to show that the techniques are significantly more efficient in comparison to existing techniques.

A 2-D fully nonlinear numerical wave tank (NWT) is developed to investigate the Bragg resonance scattered by submerged multi-array breakwaters for random waves. This model is based on a boundary integral equation method with linear element scheme. The fully nonlinear free surface boundary condition is treated using the Mixed Eulerian-Lagrangian method and the 4th-order Runge-Kutta method. The incident random waves are generated by JONSWAP spectrum at one end of the wave tank. Two damping zones are deployed at both ends of the NWT to absorb the energy of the reflected and transmitted waves. In the regular wave cases, the results of Bragg reflection calculated are in good agreement with that of other experiments and numerical models. In addition, the simulated spectrum of random waves is also verified by the original input spectrum. The results of the random waves have the same trend as those of the Regular waves. The reflection coefficient for random waves at the first peak of resonance is about 70 percent of that of the regular wave, but the frequency of band width of Bragg effect has become wider and this advantage may compensate the peak reduction. Finally, we may conclude that the present model is adequate to use as a tool for coastal protection. Systematic studies for random waves propagating over series submerged breakwaters are conducted. The Bragg reflection will be enhanced with the increase of relative height, the length of bars, the number of breakwaters, and the toe angle of submerged breakwaters. In this study, it also reveals that the frequency of peak reflection for higher breakwaters has down shift phenomenon.

In this paper we develop a computational procedure to investigate linear fracture of two-dimensional problems in isotropic linearly elastic media. A symmetric Galerkin boundary element method (SGBEM), based on a weakly singular, weak-form traction integral equation, is adopted to model these fractures. In particular we consider multiple interacting cracks in an unbounded domain subject to internal pressure and remote stress. The growth of the cracks is driven by either linearly dependent injection pressures or volumes in each crack. A variety of crack geometries are investigated. / text

A novel numerical method solves the VIScous Vorticity Equation (VISVE) in 3D in order to model the Leading Edge Vortex (LEV) of propellers is proposed and implemented in this dissertation. The spatial concentration of the vorticity is exploited in the method, which is designed to be spatially compact and numerically efficient, in the meantime, capable of modeling complicated vorticity/solid boundary interaction in 2D and 3D. The numerical model can work as a viscous correction on top of the traditional Boundary Element Method (BEM) results. The proposed method is first applied in the case of a 2D hydrofoil at high angle of attack. The results are correlated with those from Navier-Stokes (N-S) simulation. The method is then used to model the LEV and tip vortex of a 3D swept wing. The results of the 3D simulation show great similarity to those from N-S. In the end, the method is applied in the case of propellers at low advance ratios. All the essential flow characteristics (LEV and tip vortex) are predicted. The objective of this dissertation is not developing a mathematically equivalent numerical method to the full-blown Reynolds-Averaged Navier-Stokes (RANS) solver, but inventing an accurate and computationally efficient tool to model the effects of the LEV on the propeller performance for engineering's purpose. / text

The effect of coupled thermo-poroelastic behavior on hydraulic fracture propagation is of much interest in geothermal- and petroleum-related geomechanics problems such as wellbore stability and hydraulic fracturing as pore pressure and temperature variations can significantly induce rock deformation, fracture initiation, and propagation. In this dissertation, a two-dimensional (2D) boundary element method (BEM) was developed to simulate the fully coupled thermo-poroelastic fracture propagation process. The influence of pore pressure and temperature changes on the fracture propagation length and path, as well as on stress and pore pressure distribution near wellbores and fractures, was considered in isotropic and homogeneous rock formations. The BEM used in this work consists of the displacement discontinuity (DD) method and the fictitious stress (FS) method. Also, a combined FS-DD numerical model was implemented for the hydraulically or thermally-induced fractures in the vicinity of a wellbore. The linear elastic fracture mechanics (LEFM) theory was adopted to numerically model within the framework of poroelasticity and thermo-poroelasticity theory. For high accuracy of crack tip modeling, a special displacement discontinuity tip element was developed and extended to capture the pore pressure and temperature influence at the tip. For poroelastic fracture propagation, a steadily propagating crack driven by fluid pressure was modeled to find the effect of pore pressure on crack path under the two limiting poroelastic conditions (undrained and drained). The results indicate that the pore pressure diffusion has no influence on the crack growth under the undrained condition because the crack propagation velocity is too fast for the diffusion effect to take place. On the other hand, its influence on the crack path under the drained condition with its low propagation velocity has significance because it induces a change in principal stress direction, resulting in an alteration of fracture orientation. For the thermal fracturing, when the rock around a wellbore and a main fracture is cooled by injecting cold water in a hot reservoir, the rapid decrease in temperature gives rise to thermal stress, which causes a crack to initiate and propagate into the rock matrix. The single and multiple fracture propagation caused by transient cooling in both thermoelastic and poro-thermoelastic rock were numerically modeled. The results of this study indicate that the thermal stresses induced by cooling may exceed the in-situ stress in the reservoir, creating secondary fractures perpendicular to main fracture. Furthermore, the faster cooling rate produces longer crack extension of the secondary thermal fractures. This implies that the faster cooling induces a higher tensile stress zone around the fracture, which tends to produce larger driving forces to make the secondary fractures penetrate deeper into the geothermal reservoir.

Elastography is an emerging functional imaging technique of current clinical research interest due to a direct relation between mechanical material parameters, especially the tissue stiffness, and tissue pathologies such as cancer. Digital Image Elasto-Tomography (DIET) is a new method that aims to develop elastographic techniques and create a simplified, improved breast cancer screening process. The elastic material information of breast tissue is reconstructed in the DIET concept from mechanically excited steady-state harmonic motion observed on the surface of the breast. While this inversion process has been traditionally approached using finite element methods, this surface-orientated problem is naturally suited to the use of Boundary Element Methods (BEMs) requiring the discretization only on the surface of the domain and on the interface of a potential inclusion. As only approximate information is available about breast tissue material parameters, this thesis presents the development of BEM based inverse problem algorithms suitable for the reconstruction of all material parameters in a proportionally damped isotropic linear elastic solid, where only the material density is known. The highly nonlinear identification process of a potential inclusion is treated through the combination of a systematic Grid-Search with gradient descent techniques. This algorithm is extended to a three-step algorithm that performs a background material parameter estimation before the subsequent identification of an inclusion and thus provides a confident indication for the differentiation between cancerous and healthy breast tissue. The development of these algorithms is illustrated by several simulation studies highlighting important reconstruction behaviors relevant to the elastographic inverse problem. A first experimental test on a silicon based breast phantom is presented.

Enclosures are a very common way to reduce noise emissions from machinery. However, enclosures display complex acoustic behavior that is difficult to predict. The research presented in this thesis uses the boundary element method in order to better understand the acoustic behavior of a partial enclosure. Insertion loss was used as the performance measure and the effect of several design factors on the overall insertion loss was documented. Results indicate that the most important factors affecting enclosure performance are the opening size, amount of absorption, and the source-to-opening distance.

Electrostatics interaction plays a very important role in almost all biomolecular systems. The Poisson-Boltzmann equation is widely used to treat this electrostatic effect in an ionic solution. In this work, a simple mixed discrete-continuum model is considered and boundary element method is used to solve for the solution. / Singapore-MIT Alliance (SMA)

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Neste trabalho utiliza-se a formulação direta do Método dos Elementos de Contorno aplicada ao problema de flexão de placas com vinculação interna. Através da utilização da teoria baseada nas hipóteses de Reissner é possível atender em cada ponto, a três condições físicas de contorno. Admite-se a aplicação de cargas transversais distribuídas e concentradas, além de momentos distribuídos em linha. Os elementos de contorno apresentam geometria linear com aproximação quadrática para as variáveis de contorno. As equações integrais dos deslocamentos são escritas para pontos de colocação dispostos fora do domínio, evitando-se assim problemas de singularidades. O sistema de equações algébricas originado da análise de placas via MEC é modificado para incorporar o enrijecimento produzido pela vinculação interna. Primeiramente é analisado o enrijecimento produzido por apoios internos pontuais ou distribuídos em áreas pequenas e, em seguida, é estudada a associação da placa com uma estrutura qualquer, formada por barras. O enrijecimento produzido por esta estrutura é obtido utilizando-se o Método dos Elementos Finitos. Finalmente, são apresentados alguns exemplos simples que mostram a boa precisão da técnica utilizada. / The direct formulation of the Boundary Element Method is applied to the analysis of internally restrained plates in bending. By employing Reissner\'s theory, the three boundary conditions are satisfied at each point. Loading conditions include concentrated or uniformly distributed loads as well as linearly distributed moments. The boundary elements are geometrically linear with quadratic approximation for the boundary variables. The displacement integral equations are written for collocation points outside the domain thus avoiding any singularity problem. The resulting system of algebraic equations is modified to include the stiffening effects. Plates with internal point restraints and restrained over small areas are analyzed as well as plates connected to others structures made up of bars. In this last case, the stiffening effect is calculated through the Finite Element Method. The results obtained in simple problems indicate the accuracy of the procedure.