Math 627 - Introduction to Parallel Computing
Fall 2013 - Matthias K. Gobbert
Presentations of the Class Projects

Friday, December 13, 2013, 01:00 p.m., Math/Psyc 401

  1. 01:05-01:20
    Low-Order Model of Biological Neural Networks as a Machine Learning Algorithm with Parallel Architecture
    Bryce Carey, Department of Mathematics and Statistics, UMBC
    The Low-Order Model of biological neural networks is a biologically plausible model of dendritic nodes, synapses, neurons, and learning and retrieving mechanisms. The model is adapted into a machine learning algorithm implemented as a C program with parallel architecture. A sample problem involving digit recognition is used as a proof of concept. Performance studies are conducted to demonstrate the benefits of parallel computing applied to the algorithm. These efforts will enable the timely acquisition of results in future studies. This work is in collaboration with advisor Dr. James T. Lo.

  2. 01:20-01:35
    Supremum Norm of Projections onto Third Order Difference Cones with Applications to Constrained Minimax Theory
    Teresa Lebair, Department of Mathematics and Statistics, UMBC
    Shape constrained estimation receives increasing consideration in applied mathematics and statistics. In this report, a B-spline estimator subject to the constraint that the third derivative is non-negative almost everywhere is proposed as an optimal estimator. This estimator's optimality is equivalent to projections onto third order difference cones being bounded in the sup-norm independent of cone dimension. The sup-norm of these projections is computed for these fixed values. Despite a large amount of computing power, it was not feasible to determine enough of these computationally expensive sup-norms to suggest that the boundedness result holds. This work is being done in collaboration with Dr. Jinglai Shen and Dr. Xiao Wang.

  3. 01:35-01:50
    Parallelization of Mergesort Algorithm and Analysis of Performance on Large Data Sets
    Georgiy Frolov, Department of Computer Science and Electrical Engineering, UMBC
    A combination of parallel computing with classical sorting algorithms can lead to significant improvements of average case performance. For the past few years commercial systems faced an enormous increase in amount of data and customers, which prompted the need for scalable algorithms. Parallel mergesort truly utilizes divide-and-conquer paradigm that it is based on by distributing the workload among a number of processes and applying classical mergesort to each individual chunk of data, regardless of data type. Performance improvements may appear insignificant for small amount of processes, however as the number of processes increases, results demonstrate instant responses which can provide an edge in today's competitive market.

  4. 01:50-02:05
    Parallelization of an UPFD-Method for Advection-Diffusion-Reaction Equations
    Sven Wallbaum, Institute of Mathematics, University of Kassel, Germany
    Advection-diffusion-reaction equations occur in modeling physical and biological systems. Often the unknowns represent properties that cannot be negative. Benito M. Chen-Charpentier and Hristo V. Kojouharov proposed an unconditionally positivity preserving finite difference scheme (UPFD) for that purpose in 2011. The key is to discretize the terms outside of the central term of the finite difference stencil at the old time step, which combines the properties of ensuring positivity of the solution and explicitness of the discretization. We briefly review the analysis for the main properties of the UPFD method, such as consistency and positivity. The consistency of the method is an issue, because it is not per se consistent, but requires minor adjustments. Afterwards, we analyze the parallel performance and convergence of the method on the basis of different test cases with respect to real life applications. This work is in collaboration with Dr. Andreas Meister and Dr. Matthias K. Gobbert.

  5. 02:05-02:20
    Parallel Performance Study of a Parabolic Test Problem Solved Using the Conjugate Gradient Method
    Timothy Munuhe, Department of Mechanical Engineering, UMBC
    The conjugate gradient method is a widely-used tool in solving large, sparse, linear systems of equations. This study uses the conjugate gradient method to solve a forced heat equation, with a known true solution, numerically in two spatial dimensions. A performance study is performed utilizing the Unix cluster tara in parallel. Results indicate that the conjugate gradient method scales well when solving the parabolic test problem. It is recommended that someone utilizing the conjugate gradient method to solve a parabolic test problem use as many processes as possible. This class project was conducted in collaboration with Dr. Matthias Gobbert.

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This page version 1.0, December 2013.