Topics in structure-preserving discretization
نویسندگان
چکیده
منابع مشابه
Structure-preserving discretization of incompressible fluids
The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the volume-preserving diffeomorphisms, and Kelvin’s circulation theorem is viewed as a consequence of Noether’s theorem associated with the particle relabeling symmetry of f...
متن کاملA Structure-preserving Numerical Discretization of Reversible Diffusions
We propose a numerical discretization scheme for the infinitesimal generator of a diffusion process based on a finite volume approximation. The resulting discrete-space operator can be interpreted as a jump process on the mesh whose invariant distribution is precisely the cell approximation of the Boltzmann invariant measure and preserves the detailed balance property of the original stochastic...
متن کاملInvariance Preserving Discretization Methods of Dynamical Systems
In this paper, we consider local and uniform invariance preserving steplength thresholds on a set when a discretization method is applied to a linear or nonlinear dynamical system. For the forward or backward Euler method, the existence of local and uniform invariance preserving steplength thresholds is proved when the invariant sets are polyhedra, ellipsoids, or Lorenz cones. Further, we also ...
متن کاملMultipole-preserving quadratures for the discretization of functions in real-space electronic structure calculations.
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in density functional theory (DFT) is given by the external potential or the pseudo-potential describing the interaction between ions and electrons. The accuracy of the collocation method...
متن کاملStructure Preserving Spatial Discretization of a 1-D Piezoelectric Timoshenko Beam
In this paper we show how to spatially discretize a distributed model of a piezoelectric beam representing the dynamics of an inflatable space reflector in port-Hamiltonian (pH) form. This model can then be used to design a controller for the shape of the inflatable structure. Inflatable structures have very nice properties, suitable for aerospace applications, e.g., inflatable space reflectors...
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ژورنال
عنوان ژورنال: Acta Numerica
سال: 2011
ISSN: 0962-4929,1474-0508
DOI: 10.1017/s096249291100002x