Dissertation Defense: John Nehls "Locally-Refined and Semi-conformal Mesh, Fully-Anisotropic Finite-Difference Time-Domain Solver: Stability, Accuracy, and Applications"

    Thursday, August 20, 2020 - 1:00pm

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    We developed a new 3D FDTD Maxwell solver for simultaneously fully-anisotropic electric and magnetic media. The algorithm's stability is proved mathematically and demonstrated numerically via eigenvalue analysis (showing that the neutral stability of the original Yee algorithm is preserved). We studied the algorithm's accuracy via a novel accuracy test for fully-anisotropic dielectrics which utilize metamaterial cloaks, a structure with known analytic solutions. We provide sufficient stability requirements for stable algorithms with diagonally-anisotropic and fully-anisotropic Drude models, developed as part of the transformation-based method—a method of incorporating non-uniform meshing into Maxwell solvers through fully-anisotropic material parameters.

    For the transformation-based Maxwell FDTD solver, we have extended it to 3D, outlined Gaussian local-mesh refinement, and introduced the utility of the semi-conformal mapping technique. Furthermore, we provide examples where each gridding technique exhibits an immense efficiency. The work lays the necessary foundation for the future of efficient and stable FDTD algorithms on unstructured meshes that, until now, have suffered from long-time instabilities.