Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences
Räbinä, J., Mönkölä, S., & Rossi, T. (2015). Efficient Time Integration of Maxwell's Equations with Generalized Finite Differences. SIAM Journal on Scientific Computing, 37 (6), B834-B854. doi:10.1137/140988759
Published inSIAM Journal on Scientific Computing
© 2015, Society for Industrial and Applied Mathematics. This is a final draft version of an article whose final and definitive form has been published by SIAM. Published in this repository with the kind permission of the publisher.
We consider the computationally efficient time integration of Maxwell’s equations using discrete exterior calculus (DEC) as the computational framework. With the theory of DEC, we associate the degrees of freedom of the electric and magnetic fields with primal and dual mesh structures, respectively. We concentrate on mesh constructions that imitate the geometry of the close packing in crystal lattices that is typical of elemental metals and intermetallic compounds. This class of computational grids has not been used previously in electromagnetics. For the simulation of wave propagation driven by time-harmonic source terms, we provide an optimized Hodge operator and a novel time discretization scheme with nonuniform time step size. The numerical experiments show a significant improvement in accuracy and a decrease in computing time compared to simulations with well-known variants of the finite difference time domain method.