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101.
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In this article, a new methodology for developing discrete geometric conservation law (DGCL) compliant formulations is presented. It is carried out in the context of the finite element method for general advective–diffusive systems on moving domains using an ALE scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles, it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed‐grid counterpart. However, only a few works proposed a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an averaged ALE Jacobians formulation is obtained. This new formulation is applied to the θ family of time integration methods. In addition, an extension to the three‐point backward difference formula is given. With the aim to validate the averaged ALE Jacobians formulation, a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Oleksiy O. Vakhnenko 《Journal of Nonlinear Mathematical Physics》2017,24(2):250-302
We summarize the most featured items characterizing the semi-discrete nonlinear Schrödinger system with background-controlled inter-site resonant coupling. The system is shown to be integrable in the Lax sense that make it possible to obtain its soliton solutions in the framework of properly parameterized dressing procedure based on the Darboux transformation. On the other hand the system integrability inspires an infinite hierarchy of local conservation laws some of which were found explicitly in the framework of generalized recursive approach. The system consists of two basic dynamic subsystems and one concomitant subsystem and it permits the Hamiltonian formulation accompanied by the highly nonstandard Poisson structure. The nonzero background level of concomitant fields mediates the appearance of an additional type of inter-site resonant coupling and as a consequence it establishes the triangular-lattice-ribbon spatial arrangement of location sites for the basic field excitations. Adjusting the background parameter we are able to switch over the system dynamics between two essentially different regimes separated by the critical point. The system criticality against the background parameter is manifested both indirectly by the auxiliary linear spectral problem and directly by the nonlinear dynamical equations themselves. The physical implications of system criticality become evident after the rather sophisticated canonization procedure of basic field variables. There are two variants of system standardization equal in their rights. Each variant is realizable in the form of two nonequivalent canonical subsystems. The broken symmetry between canonical subsystems gives rise to the crossover effect in the nature of excited states. Thus in the under-critical region the system support the bright excitations in both subsystems, while in the over-critical region one of subsystems converts into the subsystem of dark excitations. 相似文献
105.
Xin-long Luo 《Applied mathematics and computation》2010,216(6):1752-1762
This article gives a second pseudo-transient method for a special system of nonlinear equations, which arises from chemical reaction rate equations. This method uses a special second-order Rosenbrock method as the discrete difference scheme, which satisfies a linear conservation law. Moreover, it adaptively adjusts the time step in inverse proportion to an arithmetic mean of the current residual and the previous residual at every iteration step. For a singular system of nonlinear equations, under some standard assumptions, local convergence of the new method is addressed. Finally, some promise numerical results are also reported. 相似文献
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We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds. 相似文献
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K. Michael Ortmann 《Mathematical Methods of Operations Research》1998,47(3):423-449
The potential approach of value theory is extended with respect to a new characterizing property called conservation giving a clear interpretation of the potential. Many analogues between game theory and physics are presented. Particularly, there is a theorem of conservation of energy analogous to the highly important one in classical mechanics. Moreover, the Shapley-Value gets a new interpretation as the marginal contribution to a certain average in contrast to that as an average marginal contribution instead. The Banzhaf-Index can also be uniquely characterized by this approach. Finally, all results are extended to games with a continuum of players of finitely many types.Initiated in January 1995 at the Institute of Mathematical Economics, University of Bielefeld, 33501 Bielefeld, GermanyThanks to the anonymous referee for helpful comments. 相似文献
110.