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