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High order numerical methods for elliptic interface problems

Yongcheng Zhou
UCSD Department of Mathematics


Elliptic or parabolic equations with discontinuous coefficients are seenin many disciplines such aselectromagnetic, fluid dynamics and biophysics. For the accurate numericalsolutions of these equations,it is important to enforce the known jumps in the solution and/or itsgradient on the internal interfaces.Failing to do this would result in solutions of low accuracy andconvergence of low order, or even divergenceof the computation. In this talk I will briefly review the ellipticinterface problems and their numericalalgorithms. I will then introduce a novel matched interface and boundary(MIB) method and its applicationsto the solution of the electrostatic potential of macromolecules.

Tuesday, October 31, 2006
11:00AM AP&M 2402