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FDTD subgridding with higher order derivative approximations
Le, Madison M.
Le, Madison M.
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2020
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Abstract
The finite-difference time-domain (FDTD) method provides numeric solutions to analyze electromagnetic problems. This includes modeling wave propagation through urban environments, wireless communications, radio-frequency identification (RFID), and antenna design. As the operating frequency increases, the computational domains to solve these problems have grown to an unmanageable size. However, FDTD subgridding methods solve this problem without the need for excessive large memory allocation. Subgridding allows for the problem space to be divided into fine grids around articles of interest and then coarse grids elsewhere. Further accuracy improvements can be achieved with a higher order FDTD method in the coarse grids. We define the standard FDTD formulation where traditional 2nd order FDTD is used and the hybrid case when 2nd as well as 4th order FDTD formulations are used. This thesis will focus on the implementation of a new subgridding algorithm designed to simplify the complexities that arise with high frequency designs. This new FDTD subgridding algorithm will be instrumental in the reduction of memory usage and execution time for applications such as antennas, antenna arrays and electromagnetic scattering problems. Subgridding errors for a 1D, 2D, and 3D FDTD simulations are developed and presented. A correlation is seen between the increase of subgridding errors with the increase of contrast ratio (ratio between the fine and course grids) for both standard and hybrid cases. , However, a trend of error reduction when using hybrid formulations over standard formulations is apparent. For example, when increasing the contrast ratio from 1:3 to, 1:9, 1:15, or 1:27, in a 2D case, the corresponding maximum errors in the computational domain for a field component become 0.61%, 0.69%, 0.70%, and 0.71%, respectively. However, strong improvement is seen when implementing the hybrid method where the corresponding errors becomes 0.42%, 0.18%, 0.16%, and 0.15%, respectively. This shows an improvement of up to 78% when implementing a hybrid over the standard second order FDTD subgridding formulation. Additionally, an improvement of up to 96% in CPU time and up to 88% in memory savings for both the standard and hybrid FDTD simulations are achieved during this research.
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