Based on the expression specifying the deformation of a multi-component object, a component-based condensation method is developed. This further reduces the size of the matrix to be inverted from the total number of unknown displacements to the number of unknown displacements with changing boundary condition. To speed up the construction of matrices, a maximal matrix technology is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix technology and the matrix inverse update strategy, eight easily-formed characteristic matrices are defined to enhance the computation speed further. / In this thesis, an algorithm is developed for simulating the deformation of multiple objects with different material properties using the boundary element method. By tessellating the surface of a geometric model into elements, classifying all the element nodes into different groups with different attributes, and partitioning the stiffness matrix into several sub-matrices according to these attributes, a compact expression about the unknown variables is deduced. In this expression, the dimension of the system matrix has been effectively reduced compared with the traditional method. This expression shows that the deformation of a multi-component object can be simulated in a way similar to that of a single-component object. / Research on the real-time deformation of elastic models has captured wide attention and gained considerable achievement in the past two decades. Most related works focus on developing efficient ways to simulate the behavior of a single-component elastic object. However, objects are usually made up of multiple components with different material properties in practice. It is thus essential to develop efficient techniques for modeling objects which are composed of more than one material. / To make the proposed accelerated algorithm more applicable, a method for simulating the deformation of multi-component models with non-matching interfaces is developed. By applying the interpolation and extrapolation methods, the displacement data can be transferred between non-conforming interfaces. With the application of the energy conservation principle, a relationship between the internal forces on different surfaces can also be established. Together with the force equilibrium conditions and displacement compatibility conditions over the common faces of objects, the deformation of models composed of multi-material components with non-matching interfaces can be simulated. During the application of the linear interpolation method, when the mesh densities on the interfaces of the neighboring components are not the same, unexpected phenomena arise in the simulation process because of this disparity. A traction super-imposition method is adopted to enforce the force constraints on the interface. Experiments showed that this approach produces the correct results. / Zhou, Aifang. / "August 2007." / Adviser: Keh Chuen Hui. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1299. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 144-155). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We propose a formulation for the update of a potential function in the level set context. This potential function is non-physical off the bubble surface but consistent with the physics on the bubble surface. We consider only axisymmetric cavitation bubbles in this paper. Included in the paper are some preliminary results and findings. / Singapore-MIT Alliance (SMA)

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping. / Singapore-MIT Alliance (SMA)

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

A time-domain model was developed to predict the fluid/structure interaction of a three-dimensional deformable body in a fluid domain subject to long-crested finite amplitude waves. These nonlinear waves induce transient motion in the body. In turn, the interaction of the body with the waves modifies the wave field, causing additional motion in the body. A time-domain simulation was required to describe these nonlinear motions of the body and the wave field. An implicit three-dimensional time-domain boundary element model of the fluid domain was developed and then coupled iteratively with a finite element model of the deformable body. Large body hydrodynamics and ideal fluid flow are assumed and the diffraction/radiation problem solved. Either linear waves or finite amplitude waves can be treated in the model. Thus the full nonlinear kinematic and dynamic free surface boundary conditions are solved in an iterative fashion. To implicitly include time in the governing field equations, Volterra's method was used. The approach is similar to that of the typical boundary element method for a fluid domain where the boundary element integral is derived from the governing field equation. The difference is that in Volterra's method the boundary element integral is derived from the time derivative of the governing field equation. The transient membrane motions are treated by discretizing the spatial domain with curved isoparametric elements. Newton-Raphson iterations are used to account for the geometric nonlinearities and the equations of motion are solved using an implicit numerical method. Examples are included to demonstrate the validity of the boundary element model of the fluid domain. The conditions in a wave channel were numerically modeled and compared to sinusoidal waves. The interaction of a submerged rigid horizontal cylinder with water waves was modeled and results compared to experimental and numerical results. The capability of the model to predict the interaction of highly deformable bodies and water waves was tested by comparing the numerical model to large-scale physical model experiment of a membrane cylinder placed horizontally in a wave channel. / Graduation date: 1992

<p>Steady-state sound fields in enclosures, with specular and diffuse reflection boundaries, are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics that are orthogonal on the half-space. The amplitudes of these harmonics are determined by a Lagrange multiplier method to satisfy the energy conservation integral constraint. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Monotonic convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. The method is very computationally efficient. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and a broadband image method, demonstrating high accuracy. The method of absorption scaling is verified for complicated 3-D cases, and showing that the spatial variation in rooms is largely determined by source position and the relative distribution of absorption, but not the overall absorption level.</p> / Dissertation

This research investigates effects of tensile stresses in liquids. Areas of application include bearing lubrication and polymer processing, in which liquids may be subjected to hydrostatic tension or large shear stresses. A primary thrust of this research is the development of a criterion for liquid failure, or cavitation, based upon the general state of stress in the liquid. A variable pressure, rotating inner cylinder, Couette viscometer has been designed and used to test a hypothesized cavitation criterion. The criterion, that cavitation will occur when a principal normal stress in a liquid becomes more tensile than some critical stress, is supported by the results of experiments with the viscometer for a Newtonian liquid. Based upon experimental observation of cavitation, a model for cavitation inception from crevice stabilized gas nuclei, and gaseous, as opposed to vaporous, cavitation is hypothesized. The cavitation inception model is investigated through numerical simulation, primarily using the boundary element method. Only Newtonian liquids are modeled, and, for simulation purposes, the model is reduced to two dimensions and the limit of negligible inertia is considered. The model includes contact line dynamics. Mass transport of dissolved gas through the liquid and in or out of the gas nucleus is considered. The numerical simulations provide important information about the probable nature of cavitation nucleation sites as well as conditions for cavitation inception. The cavitation criterion predicts cavitation in simple shear, which has implications for rheological measurements. It can cause apparent shear thinning and thixotropy. Additionally, there is evidence suggesting a possible link between shear cavitation and extrusion defects such as sharkskin. A variable pressure capillary tube viscometer was designed and constructed to investigate a hypothesized relationship between shear cavitation and extrusion defects. Results indicate that despite the occasional coincidence of occurrence of cavitation and sharkskin defects, cavitation cannot explain the onset of extrusion defects. If nuclei are removed, then liquids can withstand a negative hydrostatic pressure. A falling body viscometer has been constructed and used to investigate the effect of negative pressures on viscosity. It is found that current pressure viscosity models can be accurately extrapolated to experimentally achievable negative pressures.

Based on a full-wave formulation, a vector boundary element method (VBEM) is proposed to model the photonic crystal fibers (PCFs) (microstructured fibers). The accuracy and efficiency of the approach are confirmed by comparing the results calculated with those in previous literatures. With employing the VBEM, the guiding characteristics, including the effective indexes, vector mode patterns, and the polarization properties of the PCFs are investigated. There polarization characteristics of the PCFs with elliptical air holes (EPCFs) and the one ring air-hole EPCF embedded in the step-index core are studied and discussed. In addition, based on the VBEM formulations, a novel and efficient numerical approach to calculate the dispersion parameters of the PCFs is also proposed. The effect of the PCF geometrical structure on the group velocity dispersion property is reviewed, and then the one-ring defect and two-ring defect PCFs are studied and designed for the ultra-flattened dispersion applications. As an example, a four-ring (two-ring defect) PCF with flattened dispersion of ¡Ó0.25 ps/km/nm from 1.295£gm to 1.725£gm wavelength is numerically demonstrated.

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.