A Boundary Meshless Method Using Chebyshev Interpolation and Trigonometric Basis Function for Solving Heat Conduction Problems

A boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two-stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution, respectively. As a result, no fundamental solution is required and the closed form of approximate particular solution is easy to obtain. The effectiveness of the proposed computational scheme is demonstrated by several examples in 2D and 31). We also compare our proposed method with the finite-difference method and the other meshless method showed in Sarler and Vertnik (Comput. Math. Appl. 2006; 51:1269-1282). Excellent numerical results have been observed. Copyright (C) 2007 John Wiley & Sons, Ltd

Engineering Analysis with Boundary Elements 31 The method of fundamental solutions for problems of free vibrations of plates

Abstract In this paper a new boundary method for problems of free vibrations of plates is presented. The method is based on mathematically modelling of the physical response of a system to external excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. So, contrary to the traditional scheme, the method described does not involve evaluation of determinants of linear systems. The method shows a high precision in simply and doubly connected domains. The results of the numerical experiments justifying the method are presented.

Vibration Analysis of Arbitrarily Shaped Membranes

Abstract: In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes: Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of some norm of the solution. In the particular case of a homogeneous membrane the method of fundamental solutions (MFS) is proposed as an effective solver of such BVPs in domains of a complex geometry. For non-homogeneous membranes the combination of the finite difference method and conformal mapping is used as a solver of the BVPs. The results of the numerical experiments justifying the method are presented

Trefftz Spectral Method (QTSM) for the stokes problem

Biblioteca Centrale CNR / CNR - Consiglio Nazionale delle RichercheSIGLEITItal