AMSC 663-664 Projects, 2005-2006
Below are the links to each student's AMSC 663-664 project webpage.
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Christopher D. Blakely
(lisztian"at"math.umd.edu)
Project Title:
The Hybrid Meshless/Spectral-Element
Shallow-Water Model
Project Supervisors: Ferdinand Baer (Meteorology)
and John E. Osborn (Mathematics)
Abstract: The purpose of this proposed research will
focus on constructing an innovative powerful and robust hybrid
approximation method for numerical geophysical fluid dynamics.
To accomplish such a task, we will focus on implementing the
hybrid method on the shallow-water equations which provide a
useful model to global climate modeling because their solutions
include nonlinear effects and wave structures similar to those of
the full primitive equations of the atmosphere.
Context: A primary objective of the current climate
community and its sponsors is to create accurate predictions of
future global climate on decadal to centennial time scales and a
broad spectrum of space scales by improving regional scale
performance and accuracy. In order to do this, innovative
methods for localized approximation and scaling must be
considered and coupled with efficient global approximations such
as the spectral-element method.
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Stephen M. Clark
(smclark"at"math.umd.edu)
Project Title:
Simulation of Population Dynamics on a River Network
Project Supervisor:
William Fagan (Biology)
Abstract: The goal of this project is to build a code
that can simulate population movement and disease dynamics on a
river network. Disease dynamics will be locally described by the
SEIR model or variants thereof. The river network will be
modeled by a graph, perhaps using fractal geometry to model the
tributary network. Population movement will be modeled by
discrete convection and diffusion processes on this graph.
Context: Many models of population movement and disease
dynamics are coupled system of reaction-convection-diffusion
(SEIR) partial differential equations often posed on rectangular
spatial domains. These models must be extended to geometries
that are better suited for modeling populations on river networks.
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Ryan B. Harvey
(rbharvey"at"math.umd.edu)
Project Title:
Auditory Scene Analysis
Project Supervisor:
Shihab A. Shamma (Electrical and Computer Engineering)
Abstract: The question of how many sound sources
generated the sound we hear each moment is a difficult one, but
one which our auditory system tackles with considerable success
consistently. This problem, known as auditory scene analysis, is
of import to the design of hearing aids, cochlear implants,
speech recognition systems and digital signal processing packages
and finds application in fields as diverse as psychology,
engineering, national security and intelligence. The proposed
project is to develop software implementing a framework for
testing models of scene analysis, as well as two current models,
on a high-performance machine, namely the IBM SP/2 parallel
machine in the Center for Scientific Computation and Mathematical
Modeling.
Context: This software project is motivated by the
desire to understand how auditory processing happens in the human
brain. Scene analysis, a natural, important piece of the puzzle
of how we view our environment, is a difficult problem requiring
the analysis of several cues, including pitch, onset, spatial
location, spectral envelope, and others. Attention and learning
mechanisms within the brain also contribute. All of these
processes come together to form a complex mechanism which is
difficult to reveal. This software will help researchers to
better understand the underlying mechanisms by providing a
framework in which to test new models, and by providing two
current models to test on various stimuli.
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Charles E. Martin
(martince"at"math.umd.edu)
Project Title:
Using Swarm Intelligence to Generate
Artificial Neural Networks
Project Supervisor:
James A. Reggia (Compter Science)
Abstract: In this project we will develop software that
utilizes aspects of biologically inspired computing as a
nontraditional approach to the generation and evolution of
artificial neural networks, (neural networks). Specifically,
principles from swarm intelligence and genetic algorithms or
programming will be applied to generate and evolve a two
dimensional neural network into a specified architecture. The
model, and the software based on it, will account for the
geometry as well as the topology of the network. In addition to
providing a novel means of encoding neural networks and exploring
different architectures, this project is intended to add to our
understanding of the relationship between the microscopic rules
governing the interactions of a particle system consisting of
locally interacting autonomous agents and the resultant
macroscopic behavior.
Context: Many systems in the natural world exhibit very
complex behavior. Yet these systems often consist of relatively
simple components that interact with each other according to
simple rules. Such situations arise frequently in biological
systems, where a group of simple, locally interacting creatures
behaves in a qualitatively straight forward manner at the level
of the individual but the group exhibits very complex behavior
and problem solving capabilities. Some examples include, the
ability of ants to find the shortest path to a food source and
the coordinated movement of schools of fish. This phenomena of
simple microscopic rules giving rise to complex macroscopic
behavior in groups of living entities is particularly interesting
in light of the fact that such systems often lack any centralized
control. The underlying principles of many of these
"self-organizing" biological systems that exhibit intelligent
behavior at the group level, ("swarm intelligence"), are being
studied so that they may be implemented in alternative problem
solving methods.
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Patrick Rabenold
(rabenold"at"math.umd.edu)
Project Title:
Parallel Adaptive Mesh Refinement for
the Incompressible Navier Stokes Equations
Project Supervisors:
Elias Balaras (Mechanical Engineering)
Abstract: Adaptive mesh refinement (AMR) enables a
spatially discretized grid to be refined in local regions that
require finer grids to resolve the flow. Using a block refinement
process, the sub-grids naturally decompose the domain, which are
used to extend the method to parallel processing. For this
project, we propose to implement a second-order projection method
to solve the incompressible Navier-Stokes equations. The spatial
grid will be adaptively refined using the PARAMESH package, and
an iterative multigrid method will be explored for the solution
of the method's associated elliptic equation.
Context: Numerical solutions of the incompressible
Navier-Stokes equations for flows involving complex geometries
are of practical importance in many engineering applications. The
computational cost of numerically solving the equations is
greatly affected by the spatial grid size required to accurately
resolve the complex fluid motions caused by and within the
near-wall region. This is especially true as the Reynolds number
is increased. However, the flow in the remaining regions of the
domain are likely to be relatively smooth over large time
intervals. AMR adaptively refines and de-refines local regions of
the grid in order to meet the requirements of the flow, without
the entire spatial grid resolution being dependent on the regions
of complexity.
- David Schug
(dschug"at"math.umd.edu)
Project Title:
Automated Photogrammetry Using a Particle Filter
Project Supervisors:
Rama Chellappa (Electrical and Computer Engineering, Compter Science)
and Ankur Srivastava (Electrical and Computer Engineering)
Abstract: Photogrammetry uses a sequence of images to
measure the relative position and orientation of objects with
respect to each other or to some specified origin. Manual
tracking of these targets is labor intensive, so automated
tracking is imperitive. The particle filter provides a robust
algorithm to meet automatic visual tracking and recognition needs
from a single sensor in two dimensions. The proposed project is
to built a tool that extends this technology to multiple sensors,
thereby providing postion data in three dimensions.
Context: This project is motivated by the desire to
quickly visualize and understand the relationships of important
objects in sequences of images. Whether human faces,
automobiles, or weapons, this project will give engineers and
scientists a tool to aquire necessary data.
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