Data and Time 
May 10 , 2012, 3:004:15 PM 
Location 
Bahen Centre (BA), Room 4164

Host 
Leon Yuan 
Modelling Material Interfaces and Boundary Conditions in HighOrder
FiniteDifference Methods
Roberto Armenta
The Edward S. Rogers Sr. Department of Electrical and Computer Engineering (Electromagnetics)
Abstract:
When numerically solving electromagnetic problems using finitedifference
methods, the enforcement of boundary conditions plays a dominant role in
the performance of the overall algorithm. Finitedifference methods are
created by substituting the partial derivatives in the differential form of
Maxwell's equations with discrete approximations. Creating discrete
finitedifference approximations of Maxwell's equations at material
interfaces and at the outer boundaries of a given problem can be a
challenging task since the employed approximations must enforce the
appropriate boundary conditions correctly. The most important recent
development in finitedifference methods has been the introduction of
finitedifference approximations of variable accuracy. By using
finitedifference approximations of variable accuracy, it is possible to
increase the accuracy of the numerical results without making the
discretisation grid finer. In most computer architectures the ability to
change the accuracy of the employed finitedifference approximations can
considerably improve the performance of the overall algorithm. The use of
variable or highorder approximations was originally proposed in the late
1990s, and, initially, all the associated techniques to enforce boundary
conditions were developed using exclusively uniform rectangular grids.
Until fairly recently it was not clear how to enforce boundary conditions
with a highorder of accuracy even on nonuniform onedimensional grids.
The reason behind this is that the role that the grid structure plays in
the enforcement of boundary conditions was not clearly understood. In this
seminar this role will be examined using simple onedimensional
transmissionline structures. In the process two newly developed methods
for enforcing impedance boundary conditions and enforcing the continuity of
the voltage and current at material interfaces will be introduced. To make
the discussion accessible to everyone, everything will be explained
starting from the transmissionline equations as introduced in most
undergraduate textbooks. By the end of the seminar, the attendees should be
able to understand why the term *highorder* is so often used in the
advertisement of commercial packages.
Biography:
Roberto Armenta is a PhD student in the Electromagnetics group under the
supervision of Prof. Costas D. Sarris and is working on the numerical
solution of Maxwell's equations. 
