Math 621  Numerical Analysis II
Numerical Methods for Partial Differential Equations
Spring 2001  Matthias K. Gobbert
Project Presentations
This page can be reached via my homepage at
http://www.math.umbc.edu/~gobbert.
Program for Day 1
Tuesday, May 08, 2001, 07:0008:50 p.m., MP 401

07:0507:30
Effective Insulation of a Planting Box
Alexandra L. Ward
We consider the problem of planting a tree in a planting box located near
a pipe line carrying hot steam. Heat is transfered from the steam line
to the surrounding ground, including the planting box. We consider the
effect that lining two sides of the box with insulation has on the
temperature distribution over the area.
Download postscriptfile of the report.

07:3007:55
Calcium Ion Diffusion in Cardiac Cells
Alexander L. Hanhart
The propagation of calcium ions in cardiac
cells is modeled by a system of three reaction diffusion equations.
Calcium ions are released at certain points in the cell according to a
probability function that relies on the concentration of the ions.
Unfortunately, this creates a discontinuous forcing term in our system
that relies on the delta function. However, using finite elements, we can
work our way around this problem. This talk serves as an introduction
to the problem, as well as outlining a finite element solution method,
and presenting results based on this method.
Download postscriptfile of the report.

07:5508:20
Finite Element Method in Truss Analysis
Jiaqiao Hu
From the physical point of view, we will formulate the
differential equation of a linear elastic bar in one dimension.
Further, we will develop its variational formulation. Then by
introducing the vector transformation and the finite element
method, we will see how these can be appied in a 2dimensional
bridge truss analysis problem.
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08:2008:45
Temperature Response at the Midplane of a Cylindrical Shell
Samuel G. Webster
The spread of heat energy throughout an isotropic solid is a
common physical occurrence. It is known that heat diffuses across such a
solid until it reaches a state of equilibrium. Mathematically, this
evolutionary process can be represented by the diffusion equation.
Using the finite element method, we seek to measure the temperature
response at the midplane of a cylindrical shell after a sudden change
in internal surface temperature. The accuracy of these parabolic
solutions is then verified by a comparison to a theoretical prediction, as
well as by the existence of second order convergence.
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Program for Day 2
Thursday, May 10, 2001, 07:0008:50 p.m., MP 401

07:0507:30
Bifurcation from the Set of Equilibria of the
ReactionDiffusion Equation
Valeriy R. Korostyshevskiy
We study the behavior of steadystate solutions of the nonlinear
reactiondiffusion equation. The main point of interest is how the
system performs depending on the values of scalar parameter(s).
To find that we use specific software packages that allow us to
make significant conclusions.
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07:3007:55
Putting a Freeze on the Concrete Island Drilling System
Tracy E. Thoma
This paper explores the application of the finite
element method to the PDE known as the heat equation. The physical
problem at hand involves a concrete island drilling system with embedded
water baths, which supports a bargemounted drilling rig. The entire
platform is placed in the ocean, which can drop to temperatures of
60 degrees F in the Arctic. If the water baths in the concrete freeze,
the walls will fracture. This situation can be avoided with the use of
insulation, as will be shown by determining the temperature throughout the
system via the finite element method.
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07:5508:20
Use of Galerkin Method and AUTO to find Solution Branches of the
CahnHilliard Equation
Jennifer E. Deering
The CahnHilliard Equation is introduced. The Galerkin method is
applied to the equation to produce a system of ordinary differential
equations. AUTO is then used to find solution branches. This work is
intended to reproduce some results found by S. MaierPaape and U. Miller.
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08:2008:45
A Feasibility Study in Estimating Magnetic Field and Fluid Velocity
Patterns Just Beneath the CoreMantle Boundary from Surface Magnetic Field
Measurements via the Radial MotionalInduction Equation
Terence J. Sabaka
We explore the feasibility of inferring fluid velocity and initial
magnetic fields just beneath the coremantle boundary (CMB) from magnetic
measurements at Earth's surface via the radial motionalinduction equation
(RMIE), a hyperbolic transport equation describing magnetic field
sustainment through field advection by highly conductive molten metal in
the core. Given spectral field models are recovered exactly from a
perturbed initial guess by nonlinear leastsquares analysis of radial
surface data synthesized from these models, where partial derivatives are
obtained by solving systems of coupled ODEs in time resulting from
spectral decompositions of the RMIE, and related equations, in space.
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Copyright © 2001 by Matthias K. Gobbert. All Rights Reserved.
This page version 2.6, May 2001.