In this dissertation, several extensions for two popular electromagnetic simulation methods: finite-different time-domain (FDTD) and finite-element time-domain (FETD), are presented. These extensions aim to increase the geometrical flexibility and modeling capabilities in simulation of Maxwell’s equations. Since straight-forward extensions to these methods produce numerical artifacts that pollute the results and reduce accuracy, alternative strategies have been sought. Various methodologies are explored here to address these issues: A E-B mixed-vector FETD implementation based on first order Maxwell equations is introduced. In this method a mix of electric and magnetic field variables are used, where an edge element expansion is used for the electric field and face element expansion is used for the magnetic field. Compared to the standard FETD methods, it can produce several advantages without any significant computational drawback: (i) it eliminates the spurious linear growth in time that may exist in the standard schemes; (ii) it produces energy-conserving schemes under appropriate time-discretization; (iii) it can be easily extended to frequency-dispersive media; (iv) it provides a natural path for hybridization with FDTD. Exploiting item (iii), E-B mixed-vector FETD is extended to inhomogeneous doubly-dispersive media. A conformal-PML implementation is also proposed for efficient simulation of open-domain boundaries by significantly reducing the buffer regions in the computational domain. Despite the advantages, finite-element simulations require solution of a linear system of equations which, in most practical problems, highly computationally intense. A hybrid FDTD-FETD method is introduced to alleviate this issue. The hybridization can result in significant optimization in computational cost by assigning detailed portion of the computational domain to FETD, while assigning the remaining to FDTD. Finally, a subgridding by domain-overriding (SGDO) methodology for full electromagnetic particle-in-cell (PIC) simulations is presented. Combined with relaxation methods, SGDO can produce significant improvements in PIC simulation accuracy.

Time-domain solvers for complex-media electrodynamics and plasma physics

We discuss the extension of an exact charge-conserving particle-in-cell (PIC) algorithm based on unstructured grids to the relativistic regime. The present PIC algorithm is based on the representation of grid-based variables such as fields, currents, and (nodal) charges as discrete differential forms of various degrees. In gather and scatter steps, Whitney functions are used as spatial interpolators from grid-based variables to kinetic variables. In the push step, Boris method is adopted to efficiently incorporate relativistic effects into the particle updates. Computational example of a plasma ball expansion and synchrotron charge acceleration are used to illustrate the proposed algorithm in the relativistic regime.

Charge-conserving relativistic PIC algorithm on unstructured grids

1d pic simulation of plasma cathode

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1d pic simulation of plasma cathode