Development of an optimized numerical wavenumber Maxwell’s equation solver in curvilinear coordinates
Date Issued
2011
Date
2011
Author(s)
Mei, Chia-Min
Abstract
In this thesis, a finite-difference time domain solver is presented for solving the Maxwell''s equations in curvilinear coordinates.The scheme formulated in time domain and non-staggered grid system can
theoretically preserve zero-divergence condition and optimized numerical wavenumber characteristics.
To accommodate the Hamiltonian structure in the Maxwell''s equations, the time integrator employed in the current semi-discretization falls into the symplectic category.
The inherent local conservation laws are also retained discretely all the time.To reduce the numerical error from the coordinate transformation in complex domain,
the Jacobian-preserving compact scheme is used in this thesis.
The integrity of the finite difference time domain method for solving the Maxwell''s equations in two-dimensional curvilinear coordinates that are amenable to the exact solutions. The results with good rates of convergence are demonstrated for all the investigated problems.
For simulating wave problems on open domain, in this thesis, the Perfectly matched layer (PML),
Total-field-Scattered-field (TF/SF) and Level Set method are employed for solving scattering problems (2D (TM) Mie scattering problem). The results simulated from the proposed method agree well with other numerical and experimental results for the chosen problems.
Finally, this scheme to other scattered structure problems is applied.
Subjects
finite-difference time domain
non-staggered grids
curvilinear coordinates
divergence free
Type
thesis
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