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Center for Nonlinear Studies |
Recent discoveries of resonance phenomena in photonic crystals has led to the need for accurate mathematical models of periodic electromagnetic scattering. There is hope that these crystals will prove to be useful in optical devices. There are various numerical issues associated with solving Maxwell's equations in a 3D periodic setting. I will outline the development of a highly accurate numerical method using the Mueller boundary integral formulation of Maxwell's equations. The Green's function is treated with Ewald summation to accelerate its convergence and to help isolate and analyze its singularities. The accuracy is achieved as singularities are isolated through the use of partitions of unity, leaving smooth, periodic integrands that can be evaluated with high accuracy using trapezoid sums. The removed singularities are resolved through a transformation to polar coordinates. The method relies on the ideas used in the free space scattering algorithm of Bruno and Kunyansky.
Host: Marianne Francois, CCS-2: COMPUTATIONAL PHYSICS AND METHODS, mmfran@lanl.gov