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Asymptotic modeling of composite materials with thin coatings by using complex variables

Presented by: 
Sonia Mogilevskaya University of Minnesota
Thursday 12th December 2019 - 14:00 to 14:30
INI Seminar Room 1
Co-Authors: Svetlana Baranova (University of Minnesota) Dominik Schillinger and Hoa Nguyen (Leibniz Universität Hannover�)

Recent advances in surface chemistry made it possible to create materials with ultrathin high-performance coating layers. Numerical modeling of such structures is a challenging task, as accurate resolution of thin layers with standard continuum-based numerical methods, e.g. FEM or BEM, would require prohibitively fine mesh sizes. To avoid this, it has been proposed in the literature to replace a finite-thickness coating layer by an interface of zero thickness and model the associated jump conditions in the relevant fields. The existing models, however, are low order accurate with respect to the thickness of the layer. The reasons for this considerable limitation are related to theoretical difficulties in constructing accurate higher-order interface models and to computational difficulties in integrating these models into standard FEM formulations characterized by low regularity conditions for the involved fields and geometry.

This talk presents a) a new complex variables based approach in developing arbitrary orders interface models for two-dimensional potential problems involving thin isotropic interphase layers and b) a new variationally consistent FEM discretization framework to naturally deal with higher-order derivatives on complex surfaces. Theoretical and computational benefits of the proposed approach will be discussed.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons