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: 534-6932; 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 in-class presentation.
• Grades: Determined by the attendance of lectures, participation in class discussions, and the course work.

A Tentative List of Topics

References

Class Projects

• The implementation of the quasicontinuum method. One-dimensional or two-dimensional, simple lattices.
• A two-scale method for stiff systems of ODE with slow and fast variables. Numerical test of different macro-micro solvers and force estimators. Comparison with some other methods for stiff ODE systems.
• A two-scale method for one-dimensional or two-dimensional elliptic homogenization problem. Numerical implementation.
• The level-set method with the finite-difference discretization for a simple, two-dimensional problem of moving interface.
• A simple phase-field model: formulation, finite difference methods, and sharp-interface-limit analysis.
• Analytical solutions of the Poisson-Boltzmann equations with special geometry. Explore numerically why the ionic density is overestimated by this model.
• Stable numerical methods for high-order 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.