Download Meshfree methods for partial differential equations IV by Michael Griebel, Marc Alexander Schweitzer PDF

By Michael Griebel, Marc Alexander Schweitzer

The numerical therapy of partial differential equations with particle tools and meshfree discretization ideas is a really lively learn box either within the arithmetic and engineering group. as a result of their independence of a mesh, particle schemes and meshfree tools can care for huge geometric adjustments of the area extra simply than classical discretization suggestions. in addition, meshfree equipment supply a promising process for the coupling of particle types to non-stop types. This quantity of LNCSE is a suite of the complaints papers of the Fourth foreign Workshop on Meshfree equipment held in September 2007 in Bonn. The articles handle the various meshfree equipment (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their software in utilized arithmetic, physics and engineering. the quantity is meant to foster this very energetic and intriguing sector of interdisciplinary learn and to give contemporary advances and ends up in this field.

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Meshfree methods for partial differential equations IV

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Along y = 3a the displacements are prescribed, and along x = 3a the tractions are prescribed, in accordance with the exact solutions given above. The four uniform grids shown in Fig. 3 are employed for convergence study and the results are plotted in Fig. 4. For such uniform grids, stresspoint integration displays excellent convergence in both displacement and energy which are almost comparable to those of full integration. This conforms with the conclusions of the convergence properties of stress-point integration in uniform grid given in [15].

In addition to ensuring convergence, and maintaining the large time steps afforded by the Lagrangian convection of particles, the present use of a mesh enables fast calculations of differential operators and the introduction of a novel waveletbased, multiresolution particle method. The method is implemented efficiently in massivley parallel computer architectures and its capabilities are demonstrated in simulations of aircraft wakes. References 1. J. T. Beale, On the accuracy of vortex methods at large times, in Proc.

The stabilization schemes studied are least-square stabilization (LSS) [5, 15], Taylor series expansion based stabilization (TEBS) [16–18] and the finite increment gradient (FIG) stabilization [19]. The relationships between these stabilization techniques are clearly brought out by our formulations. Numerical results show that LSS and TEBS successfully improve the convergence and stability properties of stress-point integration while the FIG fails. Moreover, the superiority of stabilized stress-point integrations over the stabilized nodal integrations is also clearly demonstrated by our numerical examples.

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