In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
In this work we consider a model for pattern-producing vegetation in semi-arid regions of the world proposed by Klausmeier. It is a coupled nonlinear diffusion-advection evolutionary PDE system describing the vegetation density and water amount. The model was studied extensively by J.Sherratt who took into consideration the field data for...
Current trends in integrated circuit technology are continuing towards physically smaller components and related structures. Interconnects between circuit components have reached sub-micron dimensions which can not be modeled accurately by the current ideal microstrip analysis based techniques. These techniques often assume that the structure being modeled is perfectly conducting, smooth,...
A new CAD-oriented methodology for the full-wave broadband characterization of coupled microstrip structures for RF/microwave and high-speed digital circuits is presented. The characterization methodology is based on the finite difference time domain (FDTD) technique combined with a systematic extraction procedure using the normal mode approach and multiport network concepts. The...
Water is one of the most biologically and economically important substances on Earth. A significant portion of Earth's water subsists in the subsurface. Our ability to monitor the flow and transport of water and other fluids through this unseen environment is crucial for a myriad of reasons.
One difficulty we...