Abstract
A multidomain Legendre–Chebyshev spectral method is developed for solving two dimensional Maxwell’s equations in inhomogeneous media with discontinuous electromagnetic waves. The method keeps spectral accuracy being not affected by the discontinuity of solutions. We construct a reasonable weak form which deals with the interface conditions similar to the natural boundary condition. Polynomial spaces of different degrees are used to approximate the electric and magnetic fields so that they can be decoupled in computation, and the optimal error estimate is obtained which improves the previous results. Numerical examples confirm the higher accuracy compared with other related method.
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