IEEE Antennas and Propagation Society Symposium, 2004., 2004
ABSTRACT The ability to model features that are small relative to the cell size is often importan... more ABSTRACT The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In principle, an unstructured grid could be used to resolve these small features. However, the increase in number of unknowns can be prohibitive. Thus, the development of accurate models that characterize the physics of the feature without the need for a highly resolved grid is essential. Practical systems possess narrow cracks and gaps that can be challenging to include in an analysis. Therefore, subcell modeling techniques have been proposed for thin slots. It has been shown that a unified approach for modeling thin wires and thin slots is possible. We show how to generalize the thin wire algorithm previously presented (Edelvik, F. et al., IEEE Trans. Antennas Propag., vol.51, no.8, p.1797-1805, 2003) to model arbitrary thin slots. Our interpolation technique used for arbitrarily located and oriented wires is successfully applied to thin slots. Allowing the slots to run arbitrarily in the grid and not aligned with the edges gives considerable modeling flexibility when including these subcellular structures in the simulations. A symmetric coupling between field and slot, and between field and wire, makes it possible to prove that the fully discrete field-wire-slot system is unconditionally stable.
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2004
Stability analysis of the finite-di erence time-domain (FDTD) method is usually performed using v... more Stability analysis of the finite-di erence time-domain (FDTD) method is usually performed using von Neumann analysis, where a necessary condition for stability is obtained by requiring the amplitude of discrete Fourier modes defined on the grid to remain bounded. However, this limits the analysis to homogeneous materials, equidistant grids and unbounded domains. A rare situation in practical computations. In this paper we analytically derive su cient conditions for stability of FDTD using the energy method. This method does not have the restrictions of von Neumann analysis and we are therefore able to derive closed-form conditions for stability in the case of non-homogeneous and lossy dielectrics, non-homogeneous permeability and varying cell sizes. Moreover, the analysis is applied to di erent lumped elements. In addition, a discussion of advantages and disadvantages of di erent discrete energy definitions in FDTD is included.
IEEE Antennas and Propagation Society Symposium, 2004., 2004
ABSTRACT The ability to model features that are small relative to the cell size is often importan... more ABSTRACT The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In principle, an unstructured grid could be used to resolve these small features. However, the increase in number of unknowns can be prohibitive. Thus, the development of accurate models that characterize the physics of the feature without the need for a highly resolved grid is essential. Practical systems possess narrow cracks and gaps that can be challenging to include in an analysis. Therefore, subcell modeling techniques have been proposed for thin slots. It has been shown that a unified approach for modeling thin wires and thin slots is possible. We show how to generalize the thin wire algorithm previously presented (Edelvik, F. et al., IEEE Trans. Antennas Propag., vol.51, no.8, p.1797-1805, 2003) to model arbitrary thin slots. Our interpolation technique used for arbitrarily located and oriented wires is successfully applied to thin slots. Allowing the slots to run arbitrarily in the grid and not aligned with the edges gives considerable modeling flexibility when including these subcellular structures in the simulations. A symmetric coupling between field and slot, and between field and wire, makes it possible to prove that the fully discrete field-wire-slot system is unconditionally stable.
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2004
Stability analysis of the finite-di erence time-domain (FDTD) method is usually performed using v... more Stability analysis of the finite-di erence time-domain (FDTD) method is usually performed using von Neumann analysis, where a necessary condition for stability is obtained by requiring the amplitude of discrete Fourier modes defined on the grid to remain bounded. However, this limits the analysis to homogeneous materials, equidistant grids and unbounded domains. A rare situation in practical computations. In this paper we analytically derive su cient conditions for stability of FDTD using the energy method. This method does not have the restrictions of von Neumann analysis and we are therefore able to derive closed-form conditions for stability in the case of non-homogeneous and lossy dielectrics, non-homogeneous permeability and varying cell sizes. Moreover, the analysis is applied to di erent lumped elements. In addition, a discussion of advantages and disadvantages of di erent discrete energy definitions in FDTD is included.
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Papers by Fredrik Edelvik