Convergence of a Leap-Frog Discontinuous Galerkin Method for Time-Domain Maxwell’s Equations in Anisotropic Materials
We present an explicit leap-frog discontinuous Galerkin method for time-domain Maxwell’s equations in anisotropic materials and establish its convergence properties. We illustrate the convergence results of the fully discrete scheme with numerical tests. This work was developed in the framework of a more general project that aims to develop a computational model to simulate the electromagnetic wave’s propagation through the eye’s structures in order to create a virtual optical coherence tomography scan (Santos et al., 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 8147–8150, 2015).
This work was partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020; by the Portuguese Government through the BD grant SFRH/BD/51860/2012; and by the Fundação para a Ciência e a Tecnologia, I.P..
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