Systems Seminar
Fast Numerical Calculation of Static Fields by Geometric Construction
or
Where Signal Processing Meets Field Theory
Prof. Paul Milenkovic
UW ECE Department
Abstract
System theory is built on the foundation of fields and waves. Many systems
are derived from calculations of acoustic or electromagnetic fields.
Methods of system theory, in turn, can be used to calculated fields.
This work is motivated by the need to determine the acoustic transfer
function of the vocal tract from a 2-d shape of the vocal conduit derived
from x-ray measurements. In the low-frequency limit, the acoustic flow
in a duct follows streamlines, which are the solution to the static fields
problem. Static fields may be determined by 1) conformal transformation,
2) graphical field mapping, or 3) numerical evaluation by finite difference
or finite element. Method 2 is typically implemented by hand sketches and
trial and error. A novel automated, numerical implementation of method 2 is
based on the rule that the local 2-d curvature of a streamline should obey a
logarithmic relation to the distance of the streamline from the boundaries
of the duct. Projection-based linearization of this rule results in a
tri-diagonal linear system solving for the displacements of points along the
streamline, which results in a fast, rapidly-converging iterative algorithm.
I will present results on the ability of the method to cope with obstacles in
the duct. This talk is of interest to those interested in optimization methods
as well as those interested in numerical solution of static fields.
Time and Place: Wed. Sep. 30, 3:45-4:45 pm in 1227 Engr. Hall.
NOTE SPECIAL ROOM