CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Reproducing Kernel Particle and Wavelet Methods
 

SPEAKER: Wing Kam Liu, Mechanical and Civil Engineering, Northwestern University 

DATE:    Wednesday, December 6, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)



ABSTRACT

Multiple scale methods, which are based on reproducing kernel and wavelet
analysis, are developed. These permit the response of a system to be
separated into different scales; and each scale response can be examined
separately. This complete characterization of the unknown response is
performed through the integral window transform; and a space-scale and
time-frequency localization process is achieved by dilating the flexible
multiple scale window function. This flexible space-scale window function
can be constructed to resemble the well-known Smooth Particle Hydrodynamic
(SPH) methods, and unstructured multi-grid and hp-adaptive finite element
methods. Numerical examples, which include structural dynamics,
compressible flow and structural acoustics are presented to illustrate the
high accuracy of the methods, the concept of multi-resolution analysis, and
the meshless unstructured adaptive refinements.