Dr. Anna M. Spagnuolo
Associate Professor of Mathematics
Oakland University, Rochester, MI
My current studies involve numerical analysis, fluid flow in porous
media, and a focus on medical applications -- including medical
device design/simulation and in-host studies of disease dynamics as
well as epidemiology. The
mathematical models for the biology problems that I study are derived
using systems of PDEs and ODEs. In regard to the numerical
analysis work, I am focused on discovering and using algorithms
for solving PDES.
I am currently working on the NSF-funded project "Collaborative
Research: Hurricane Storm Surge Modeling on Petascale Computers,"
with the following two Ph.D. students: Michael DuChene
(Engineering) and Daniel Coffield (Mathematics) from Oakland
University. I am the PI on the Oakland University portion.
Dr. Clint Dawson from the University of Texas at Austin is the main PI
of the project and Dr. Joannes Westerink is the PI at the University of
Notre Dame. We are working on the speedup of numerical code on
Petascale computers for hurricane prediction.s
I was co-PI on an NSF grant for work on "Numerical Speedup
Using Flowpaths," where Field
Programmable Gate Arrays (FPGA's) are used to provide a cost-effective
way of
speeding up existing numerical algorithms and subsets of more general
algorithms used within them. For those interested in FPGA's, I
recommend taking the short course,
"Algorithm Design in the Era of Reconfigurable Computing," offered by
Accelogic, LLC, which is funded by an Academic/Non-Profit Grant
Program (ANG Program). For more information about Accelogic, LLC and
the short
course offerings, please see
Accelogic, LLC.
I compute using gfortran on ubuntu linux. Jorge Castro, a ubuntu
guru
rocks! He introduced me to ubuntu in August 2004. I've been very
happy
with ubuntu ever since that
time :-)
The following pictures show the transport of a Uranium plume after
it
leaks into ground water. The plume represents the saturation level of
Uranium at the particular time (years). We also see how fractures in
the medium could influence the flow pattern. We see here how the
plume heads in a diagonal direction due to the geometry of the
macroscopic permeability of the rock. This study is joint work with
Jim Douglas, Jr and Chieh-Sen Huang.
research
permeability
Below we see a comparison of 2 numerical methods in the computation of
the
saturation of uranium in ground water. The contour curves give the
saturation. We see that the method on the left (MMOCAA) shows that the
fluid really covers the region much more than the method on the
right (MMOC). This result is clear mathematically, since we can prove
that the MMOC "looses" mass in the computation of each time step.
mmocaa
NOTE: In the first saturation plots on this page, a more complicated,
locally conservative numerical method was implemented (LCELM). For the
problem of interest, there is little difference between the MMOCAA and
the
LCELM.
SELECT JOURNAL PUBLICATIONS
(with Jim Douglas, Jr. and C.-S. Huang) The approximation of
nuclear contaminant
transport in porous media, Computational and Applied Mathematics,
to
appear: (gzipped postscript) lcelmsims
or (pdf) lcelmsims.pdf
(with Jim Douglas, Jr.) The transport of nuclear contamination
in fractured porous
media, Korean J. Math, to appear: (gzipped postscript)dualpormodel or (pdf)
dualpormodel.pdf
(with Zhangxin Chen, Richard E. Ewing, and Qiaoyuan Jiang)
Error
analysis for characteristics-based methods for degenerate parabolic
problems (gzipped postscript)
degenerate
or (pdf) degenerate
(with Zhangxin Chen, Richard E. Ewing, and Qiaoyuan Jiang)
Degenerate two-phase incompressible flow V: characteristic finite
element methods (gzipped postscript)
degenerate2 or (pdf) degenerate2
(with Steve Wright) Derivation of a multiple-porosity model of
single-phase flow through a fractured porous medium via recursive
homogenization, in Asymptotic Analysis 39, Vol. 2, 2004, pp. 92--112.
(with William Lindsey, Curt J. Chipman, and Fiki Shillor) Numerical
simulations of vehicle platform stabilization,
(with Steve Wright and Peter Shi) Reiterated homogenization and the
double-porosity model, with Peter Shi and Steve Wright, Transport in
Porous Media, Vol. 59
(with Darrin Hanna, William Lindsey, and Gabrielle A. Stryker)
Modeling HIV-1 dynamics and the effects of decreasing activated
infected T-cell count by filtration, to appear in Proceedings of the
26th Annual International Conference of IEEE-EMBS, San Francisco, CA
September 1--5, 2004.
The following is work in math/biology. It illustrates the dynamics
of Vibrio cholerae in an intestine. This is joint work with Vic
DiRita
and Denise Kirschner at the University of Michigan.
Steady-state solutions
Time-Dependent solutions