Licentiate thesis 2000-005

Finite Volume Solvers for the Maxwell Equations in Time Domain

Fredrik Edelvik

October 2000

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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