Theoretical and Numerical Analysis for Non-Linear Interface Problems

Abstract

Abstract : This proposal concerns modeling, analysis, and computational simulations of some non-linear interface problems and applications, that, we believe, are of interests to DOD/ARO missions especially in the fields of computational geometry, computational fluid mechanics, non-linear dynamics, imaging processing, and inverse scattering. Most of our previous work has been focused on linear interface problems with discontinuities. We have been focusing on non-linear interface problems and applications that are of interests of DoD/ARO during the course of the project, particularly for nonlinear interface problems in MR fluids and weighted surface problems. We have successfully developed the immersed interface method for several non-linear interface problems including Poisson-Boltzmann equations on irregular domains, some variational problems, augmented approach for interface problems and problems on irregular domains.