A similar methodology is also developed for the Timoshenko beam. The frequency/wave number relationship of the continuum case can be closely simulated by using the reproducing kernel particle methods. The analysis of the wave equation shows the effectiveness of this approach. An adaptivity similar to hp-finite element method is obtained through the choice of an optimal dilation parameter. A variation in the size of the window implies a geometrical refinement and allows the filtering of the desired frequency range. The interpolation functions consist of spline functions with a built-in window which permits translation as well as dilation. In this study, a wavelet particle method based on the multiresolution analysis encountered in signal processing has been developed. 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. Compared with mesh-based methods, 1 4 meshfree methods receive much concern because field points used in this method are arbitrarily distributed and material properties are no more assigned to elements. In order to capture the important physical phenomena, p-finite elements and/or hp-finite elements are employed. Numerical methods have been widely implemented to model acoustic and hydrodynamic waves. Most theories, computational formulations, and simulation results presented are. This paper reviews several novel and older methods for coupling meshfree particle methods, particularly the elementfree Galerkin (EFG) method and the Smooth. As a powerful tool, the finite element method has been widely used in the study of complex systems. Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. 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.
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