Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
On a finite-element method for solving the three-dimensional Maxwell equations
Journal of Computational Physics
A mathematical analysis of the PML method
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
SIAM Journal on Numerical Analysis
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
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A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.