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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/33908

Title: The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations
The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations
Authors: Armenta Barrera, Roberto
Advisor: Sarris, Costas D.
Department: Electrical and Computer Engineering
Keywords: numerical techniques
finite-difference methods
material boundaries
material interfaces
artificial materials
metamaterials
FDTD
high-order methods
Issue Date: 6-Dec-2012
Abstract: The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.
URI: http://hdl.handle.net/1807/33908
Appears in Collections:Doctoral

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