The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and analysis. Our computational results indicate that 72% of the NETLIB suite problem instances are ill-conditioned. However, after pre-processing heuristics are applied, only 19% of the post-processed problem instances are ill-conditioned, and log C(d) of the finitely-conditioned post-processed problems is fairly nicely distributed. We also show that the number of IPM iterations needed to solve the problems in the NETLIB suite varies roughly linearly (and monotonically) with log C(d) of the post-processed problem instances. Empirical evidence yields a positive linear relationship between IPM iterations and log C(d) for the post-processed problem instances, significant at the 95% confidence level. Furthermore, 42% of the variation in IPM iterations among the NETLIB suite problem instances is accounted for by log C(d) of the problem instances after pre-processin

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)

Elliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive definite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive definite matrices that arise from the finite element discretization of elliptic partial differential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the finite element matrices.

Different universal methods (also called automatic or black-box methods) have been suggested to sample from univariate log-concave distributions. The description of a suitable universal generator for multivariate distributions in arbitrary dimensions has not been published up to now. The new algorithm is based on the method of transformed density rejection. To construct a hat function for the rejection algorithm the multivariate density is tranformed by a proper transformation T into a concave function (in the case of log-concave density T(x) = log(x).) Then it is possible to construct a dominating function by taking the minimum of several tangent hyperplanes which are transformed back by $T^(-1)$ into the original scale. The domains of different pieces of the hat function are polyhedra in the multivariate case. Although this method can be shown to work, it is too slow and complicated in higher dimensions. In this paper we split the $R^n$ into simple cones. The hat function is constructed piecewise on each of the cones by tangent hyperplanes. The resulting function is not continuous any more and the rejection constant is bounded from below but the setup and the generation remains quite fast in higher dimensions, e.g. n=8. The paper describes the details how this main idea can be used to construct algorithm TDRMV that generates random tuples from multivariate log-concave distribution with a computable density. Although the developed algorithm is not a real black box method it is adjustable for a large class of log-concave densities. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

To compute the expectation of a function with respect to a multivariate distribution naive Monte Carlo is often not feasible. In such cases importance sampling leads to better estimates than the rejection method. A new importance sampling distribution, the product of one-dimensional table mountain distributions with exponential tails, turns out to be flexible and useful for Bayesian integration problems. To obtain a heavy-tailed importance sampling distribution a new radius transform for the above distribution is suggested. Together with a linear transform the new importance sampling distributions lead to simple and fast integration algorithms with reliable error bounds. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

In one of the non-destructive testing techniques, Lamb waves, because of its ability to propagate a long distance and being hard to attenuate, can detect a wide range of area. However, due to its multimodal and dispersive characteristics, identifying the signals of defects during the test is often difficult. Time reversal method, a self-focusing technique, can offset the dispersion of Lamb waves and effectively focus on the spatial and temporal domain. This study applies the finite element method to stimulate the propagation of Lamb waves on an aluminum plate, selecting four sets of frequency-thickness products and two excitation types to excite the single-mode or multimode Lamb waves. This study aims to discuss the effects of modal and dispersion on the focus of the time reversal methods. The results show that 2 MHz-mm and in-plane excitation can produce numerous, more dispersive modals with the best focus effect. If we applied the time reversal method to testing the defects of Lamb waves, and the defects are circular and longitudinal notches, then, according to the results, the reflection signal amplitude of the circular defects can be highly increased. According to the test results of small-sized notches, the time reversal method cannot effectively improve the detecting ability of this defect.

Currently, data size that we have to deal with is growing bigger and bigger. This fact implies that the computing time and computing power for dealing with the data is demanded. A way to circumvent the difficulty is as follows: Divide the data into several small blocks and then process these small blocks by several computers. Therefore, we need a tool for the decomposition-coordinated procedure. Alternating direction method of multipliers (ADMM) is a powerful algorithm for the mentioned purpose and has widely used in distributed optimizations. With ADMM algorithm, a big global optimization problem can be decomposed into several small local optimization problems. ADMM algorithm has been used in several recent distributed systems such as cloud systems and distributed antenna systems. In this thesis, we aim to apply the ADMM in a distributed antenna system. For the uplink setting, we develop a distributed demodulation algorithm, where multiple base stations collaborate with each other for data detection. On the other hand, for the downlink setting, we develop a distributed beamforming design algorithm, where multiple base stations collaborate to form a beamforming for mitigating the inter-cell interference. Finally, simulations are conducted to verify the efficiency of our designs.

Recently the phenomena of Bose-Einstein condensates have been observed in laboratories, and the related problems are extensively studied. In this paper we consider the nonlinear Schrödinger equation in the laser beam rotating magnetic field and compute its corresponding energy functional under the mass conservative condition. By separating time and space variables, factoring real part and image part, and discretizing via finite difference method, the original equation can be transformed to a large scale parametrized polynomial systems. We use continuation method to find the solutions that satisfy the mass conservative condition. We will also explore bifurcation points on the curves and other solutions lying on bifurcation branches. The numerical results show that when the rotating angular momentum is small, we can find the solutions by continuation method along some particular curves and these curves are regular. As the angular momentum is increasing, there will be more bifurcation points on curves.

Wire bonding has been used in integrated circuit packaging for many decades because of its high reliability and performance. The most common metal used has been gold, but with the surge in commodity prices of gold in recent years, copper wire is now used to altered gold wire for cost saving. Many challenges have to be solved to meet its application requirement; coating is one of the applications. In this study, a 3D coated copper wire and coated Al pad is built by finite element method to simulate ultrasonic bonding and thermosonic bonding. To consider the effect of coated material to stress and strain field on ultrasonic bonding and the effect of coated material to temperature field on thermosonic bonding. Then use the Taguchi experiment method to discuss the effect on Cu-Ball and Al pad under different coated material and thickness combination. The results show that with coated material on Al pad or copper wire could reduce more than 48% of effective plastic strain after the bonding process, it obviously reduce the Al splash phenomenon in copper wire bonding. But the coated material such like palladium and nickel which have lower thermal conductivity would resist the heat transfer. And the Taguchi experiment method shows that the most effective way to reduce the effective stress during impact stage and ultrasonic vibration stage is to increase the thickness of palladium and nickel respectively, and when the thickness of coated material Au reached 0.01£gm could increase the temperature of Cu-Ball and Al pad mostly.