3aSA8. Multiresolution reproducing kernel particle methods in acoustics.

Session: Wednesday Morning, December 4

Time: 9:50

Author: Wing Kam Liu
Location: Dept. of Mech. Eng., Northwestern Univ., 2145 Sheridan Rd., Evanston, IL 60208


In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention for a realistic representation of the physics. As a powerful tool, the finite-element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-finite elements and/or hp-finite elements are employed. The reproducing kernel particle methods (RKPM) are emerging as an effective alternative due to the absence of a mesh, and the ability to analyze a specific frequency range. In this study, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. A variation in the size of the window implies a geometrical refinement, and allows the filtering of the desired frequency range. An adaptivity similar to the hp-finite-element method is obtained through the choice of an optimal dilation parameter. Preliminary analysis of the wave equation shows the effectiveness of this approach. A similar methodology is also developed for the Timoshenko beam.

ASA 132nd meeting - Hawaii, December 1996