High performance numerical modeling of ultra-short laser pulse propagation based on multithreaded parallel hardware

The focus of this study is development of parallelised version of severely sequential and iterative numerical algorithms based on multi-threaded parallel platform such as a graphics processing unit. This requires design and development of a platform-specific numerical solution that can benefit from the parallel capabilities of the chosen platform. Graphics processing unit was chosen as a parallel platform for design and development of a numerical solution for a specific physical model in non-linear optics. This problem appears in describing ultra-short pulse propagation in bulk transparent media that has recently been subject to several theoretical and numerical studies. The mathematical model describing this phenomenon is a challenging and complex problem and its numerical modeling limited on current modern workstations. Numerical modeling of this problem requires a parallelisation of an essentially serial algorithms and elimination of numerical bottlenecks. The main challenge to overcome is parallelisation of the globally non-local mathematical model. This thesis presents a numerical solution for elimination of numerical bottleneck associated with the non-local nature of the mathematical model. The accuracy and performance of the parallel code is identified by back-to-back testing with a similar serial version.

Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

Distributed algorithms for global optimization on sparse networks of arbitrary bandwidths

The optimization of resource allocation in sparse networks with real variables is studied using methods of statistical physics. Efficient distributed algorithms are devised on the basis of insight gained from the analysis and are examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Numerical modelling of agglomerate degradation

In the processing industries particulate materials are often in the form of powders which themselves are agglomerations of much smaller sized particles. During powder processing operations agglomerate degradation occurs primarily as a result of collisions between agglomerates and between agglomerates and the process equipment. Due to the small size of the agglomerates and the very short duration of the collisions it is currently not possible to obtain sufficiently detailed quantitative information from real experiments to provide a sound theoretically based strategy for designing particles to prevent or guarantee breakage. However, with the aid of computer simulated experiments, the micro-examination of these short duration dynamic events is made possible. This thesis presents the results of computer simulated experiments on a 2D monodisperse agglomerate in which the algorithms used to model the particle-particle interactions have been derived from contact mechanics theories and, necessarily, incorporate contact adhesion. A detailed description of the theoretical background is included in the thesis. The results of the agglomerate impact simulations show three types of behaviour depending on whether the initial impact velocity is high, moderate or low. It is demonstrated that high velocity impacts produce extensive plastic deformation which leads to subsequent shattering of the agglomerate. At moderate impact velocities semi-brittle fracture is observed and there is a threshold velocity below which the agglomerate bounces off the wall with little or no visible damage. The micromechanical processes controlling these different types of behaviour are discussed and illustrated by computer graphics. Further work is reported to demonstrate the effect of impact velocity and bond strength on the damage produced. Empirical relationships between impact velocity, bond strength and damage are presented and their relevance to attrition and comminution is discussed. The particle size distribution curves resulting from the agglomerate impacts are also provided. Computer simulated diametrical compression tests on the same agglomerate have also been carried out. Simulations were performed for different platen velocities and different bond strengths. The results show that high platen velocities produce extensive plastic deformation and crushing. Low platen velocities produce semi-brittle failure in which cracks propagate from the platens inwards towards the centre of the agglomerate. The results are compared with the results of the agglomerate impact tests in terms of work input, applied velocity and damage produced.

Call admission control algorithms in OFDM-based wireless multiservice networks

Orthogonal frequency division multiplexing (OFDM) is becoming a fundamental technology in future generation wireless communications. Call admission control is an effective mechanism to guarantee resilient, efficient, and quality-of-service (QoS) services in wireless mobile networks. In this paper, we present several call admission control algorithms for OFDM-based wireless multiservice networks. Call connection requests are differentiated into narrow-band calls and wide-band calls. For either class of calls, the traffic process is characterized as batch arrival since each call may request multiple subcarriers to satisfy its QoS requirement. The batch size is a random variable following a probability mass function (PMF) with realistically maximum value. In addition, the service times for wide-band and narrow-band calls are different. Following this, we perform a tele-traffic queueing analysis for OFDM-based wireless multiservice networks. The formulae for the significant performance metrics call blocking probability and bandwidth utilization are developed. Numerical investigations are presented to demonstrate the interaction between key parameters and performance metrics. The performance tradeoff among different call admission control algorithms is discussed. Moreover, the analytical model has been validated by simulation. The methodology as well as the result provides an efficient tool for planning next-generation OFDM-based broadband wireless access systems.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.