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.