Development of the Finite Difference Time Domain Method on a Lebedev Grid for Anisotropic Materials

Date
2012-12-14
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Abstract
The finite-difference time-domain (FDTD) method is derived on a Lebedev grid, instead of the standard Yee grid, to better represent the constitutive relations in anisotropic materials. The Lebedev grid extends the Yee grid by approximating Maxwell's equations with tensor constitutive relations using only central differences. A dispersion relation with stability criteria is derived and it is proven that the Lebedev grid has a consistent calculus. An integral derivation of the update equations illustrates how to appropriately excite the grid. This approach is also used to derive the update equations at planar material interfaces and domain edge PEC. Lebedev grid results are compared with analytical and Yee grid solutions using an equal memory comparison. Numerical results show that the Lebedev grid suffers greater dispersion error but better represents material interfaces. Focus is given to generalizing the concepts that make the Yee grid robust for isotropic materials.
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Keywords
Engineering--Electricity and Magnetism, Computer Science, Engineering--Electronics and Electrical
Citation
Nauta, M. (2012). Development of the Finite Difference Time Domain Method on a Lebedev Grid for Anisotropic Materials (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25689