Two unstructured finite volume solvers for the Maxwell equations in 2D and 3D are introduced. The solvers are a generalization of FD-TD to unstructured grids and they use a third-order staggered Adams-Bashforth scheme for time discretization. Analysis and experiments of this time integrator reveal that we achieve a long term stable solution on general triangular grids. A Fourier analysis shows that the 2D solver has excellent dispersion characteristics on uniform triangular grids. In 3D a spatial filter of Laplace type is introduced to enable long simulations without suffering from late time instability. The recursive convolution method proposed by Luebbers et al. to extend FD-TD to permit frequency dispersive materials is here generalized to the 3D solver. A better modelling of materials which have a strong frequency dependence in their constitutive parameters is obtained through the use of a general material model. The finite volume solvers are not intended to be stand-alone solvers but one part in two hybrid solvers with FD-TD. The numerical examples in 2D and 3D demonstrate that the hybrid solvers are superior to stand-alone FD-TD in terms of accuracy and efficiency.
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