Vrushali Bokil, Department of Mathematics, Oregon State University
Compatible Discretizations for Maxwell’s Equations in Complex Materials
In this talk, we discuss the construction of a specific compatible discretization, the Mimetic Finite Difference (MFD) method, for time domain electromagnetic wave propagation in linear dispersive media. The discretization utilizes an optimization procedure called M-adaptation to minimize numerical dispersion error. The dispersive effects are captured by appending to Maxwell's equations ordinary differential equations in time for the evolution of the macroscopic polarization in the constitutive equations for the material. These differential equations model material responses to the incident electric and magnetic fields, such as relaxation or resonance processes. The M-adaptation technique results in a MFD method with fourth order numerical dispersion error. This is joint work with Nathan Gibson in the Department of Mathematics at Oregon State University, Vitaliy Gyrya in the Applied Mathematics and Plasma Physics group at Los Alamos National Laboratory, and Duncan McGregor in the Computational Multiphysics group at Sandia National Laboratory.