MATH 273A: Scientific Computation
Fall quarter, 2005
TOPICS IN APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCE
Instructor: Bo Li

Course Announcement

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Class Information
 Lecture time and place:
1:00 pm  1:50 pm, MWF, AP&M 5829.
 Instructor: Bo Li
 Office: AP&M 5723; Phone: 5346932; Email: bli@math.ucsd.edu.
 Office hours: by appointment only.
 Textbooks/lecture notes:
No textbooks will be used. When available, lecture notes
will be distributed in the class and/or posted on the class web.
 Computer skills: Matlab, Fortran 90, or C++.
 Course work:
A few homework assignments, a possible computational project,
and a possible inclass presentation.
 Grades:
Determined by the attendance of lectures, participation in class discussions,
and the course work.


Class Projects

The implementation of the quasicontinuum method. Onedimensional or twodimensional,
simple lattices.

A twoscale method for stiff systems of ODE with slow and fast variables.
Numerical test of different macromicro solvers and force estimators.
Comparison with some other methods for stiff ODE systems.

A twoscale method for onedimensional or twodimensional
elliptic homogenization problem. Numerical implementation.

The levelset method with the finitedifference discretization for
a simple, twodimensional problem of moving interface.

A simple phasefield model: formulation, finite difference methods, and
sharpinterfacelimit analysis.

Analytical solutions of the PoissonBoltzmann equations with special
geometry. Explore numerically why the ionic density is overestimated by this model.

Stable numerical methods for highorder diffusion equations and
the prediction of scaling laws of coarsening in surface growth.
 Geometrical models of blood cells. Motion based on
the reduction of Helfrich energy functional. Numerical methods.
Research and Funding Opportunities for Graduate Students
 Graduate students who are interested in exciting researches in
applied mathematics and computational science as well as
financial support to their Ph.D. work may contact the instructor for more information.
Last updated by Bo Li on September 23, 2005.