國家理論科學研究中心學術演講

　

NCTS Seminar in

Applied Math. & Scientific Computation 

　

Speaker :       Prof. Zhilin Li 李治林
                      (North Carolina State University)

Talk (1)

　

Topic    :       Theoretical and Numerical Analysis for Some

                     Non-linear Interface Problems

　

Time     :       March 24, 2004 (Wednesday)   3:30-5:00 pm
                     (3:00 pm Tea time)


Abstract :

　

    Non-linear partial differential equations with discontinuity in the coefficient have many applications.  In this talk, I will focus on two different non-linear interface problems.  One is the the potential equation for magneto-rhological (MR) fluid that contains metal particles.  The permeability is discontinuous across the interface between the fluid and the particles.  The second problem is the weighted minimal surface problem.  We have generalized the Sneil's law for optical path to the three dimensional weighted minimal surface problem.  Numerically, we use the substitution method to solve the non-linear PDE.  Since the coefficient of the potential equation depends on the gradient of the solution, we use the maximum preserving immersed interface method coupled with multigrid solvers to solve the linearized problems.  Numerical examples will also be presented.

Talk (2)--Postponed，時間另行通知。

　

Topic     :       Augmented Techniques for Interface/Irregular

                      Domain Problems and Applications

　

Time      :       April 2 (Friday) AM 10:30~12:00

　

　

　

Abstract :

　

     In order to solve some interface/irregular domain problems, it is advantageous to use an augmented technique in which one or several intermediate variables called augmented variables are introduced. With these augmented variables, it is easier to discretize the partial differential equation. More important, fast solvers that are designed for regular problems or regular domains can be used. I will explain this technique with examples of elliptic interface problems with large jumps in the coefficient; fast Poisson/biharmonic solvers on irregular domains (interior or exterior); and two phase Stokes flows with large jump in the viscosity.  For the last example, new jump conditions of the pressure and the velocity are coupled together. The augmented approach seems to be the only way to solve the problem accurately.

　

Place     :

 R216,

Department of Applied Mathematics,
Science Building I,
National Chiao Tung University, Hsinchu

Place      : Lecture Room A,

National Center for Theoretical Sciences
4th Floor, The 3rd General Building,
National TsingHua University, Hsinchu