2019/11/02 by Helsing, Johan, Rosén, Andreas
#15A66 #45E05 #65R20 #78M15 #Analysis of PDEs (math.AP) #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.1911.00788
A new integral equation formulation is presented for the Maxwell transmission problem in Lipschitz domains. It builds on the Cauchy integral for the Dirac equation, is free from false eigenwavenumbers for a wider range of permittivities than other known formulations, can be used for magnetic materials, is applicable in both two and three dimensions, and does not suffer from any low-frequency breakdown. Numerical results for the two-dimensional version of the formulation, including examples featuring surface plasmon waves, demonstrate competitiveness relative to state-of-the-art integral formulations that are constrained to two dimensions. However, our Dirac integral equation performs equally well in three dimensions, as demonstrated in a companion paper.