Document Type


Date of Award

Fall 1-31-2005

Degree Name

Doctor of Philosophy in Applied Physics - (Ph.D.)


Federated Physics Department

First Advisor

Haim Grebel

Second Advisor

John Francis Federici

Third Advisor

Edip Niver

Fourth Advisor

Richard V. Snyder

Fifth Advisor

Daniel Ely Murnick

Sixth Advisor

Andrei Sirenko


The Finite-Difference Time-Domain (FDTD) method and Finite-Element (FEM) method are numerical techniques used for solving Maxwell's electromagnetic equations. FDTD-FEM hybrid methods opt for combining the advantages of both FDTD and FEM. In this dissertation, signal processing techniques were used to analyze the FDTD stability condition. A procedure, which reduces time-sampling error yet preserves the stability of algorithm is proposed. Both explicit and implicit time-stepping schemes were treated in the framework of the developed method. An improved version of the implicit-explicit FEM-FDTD hybrid method was developed. The new method minimizes reflection from the interface between different types of grids. A class of transfer functions with low reflection error for stable hybrid time-stepping was derived. The stability of the method is rigorously proven for a general three-dimensional case.

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