PSU Mark
Eberly College of Science Mathematics Department

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<>July 2016
June 2016
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July 5th, 2016 (10:01am - 12:01pm)
Seminar: Ph.D. Thesis Defense
Title: Fast Solvers for Incompressible Magnetohydrodynamics Systems
Speaker: Yicong Ma, Adviser: Jinchao Xu, Penn State
Location: MB114

Maxwell's equations are a set of partial differential equations (PDE) that, together with Lorentz force, form the foundation of classical electrodynamics, classical optics and electric circuits. First, we study their coupling with the incompressible Navier-Stokes equations, namely the incompressible magnetohydrodynamics system. We propose a structure-preserving finite element discretization and then design a class of robust preconditioners for the linear system by combining techniques from both functional analysis and linear algebra. Secondly, we study a practical problem related to Maxwell's equations that model the optical process in solar cells. We study the mathematical model and fast solvers for the linear system resulting from the finite element discretization. Extensive numerical experiments are carried out for the proposed algorithms for both types of PDE systems.