Multiresolution Reproducing Kernel Particle Methods in acoustics

In the analysis of complex phenomena of acoustic systems, the computational modeling requires special attention in order to give 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 hp-finite element method is obtained through the choice of an optimal dilation parameter. The analysis of the wave equation shows the effectiveness of this approach. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. A similar methodology is also developed for the Timoshenko beam.