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In this article we introduce new bounds on the e ective condition number of de ated and preconditioned-de ated symmetric positive de nite linear systems. For the case of a subdomain de ation such as that of Nicolaides (1987), these theorems can provide direction in choosing a proper decomposition into subdomains. If grid re nement is done keeping the(More)
Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE methods to the case of Hamiltonian PDEs. Their excellent long time behavior for a variety of Hamiltonian wave equations has been demonstrated in a number of numerical studies. A theoretical investigation and justification of multi-symplectic methods is still largely(More)
A new particle-mesh method is proposed for the rotating shallow-water equations. The spatially truncated equations are Hamiltonian and satisfy a Kelvin circulation theorem. The generation of non-smooth components in the layer-depth is avoided by applying a smoothing operator similar to what has recently been discussed in the context of -Euler models.
The Hamiltonian particle-mesh (HPM) method is generalized to the spherical shallow water equations, utilizing constrained particle dynamics on the sphere and smoothing with Merilees’ double-periodic FFT formulation of O(J log J) in the latitudinal gridsize. The time step for the explicit, symplectic integrator depends only on the uniform smoothing length.(More)
BACKGROUND One of the most important issues that interventional physicians address during treatment is informing patients of their treatment options. Prior to beginning treatment, patients are given this information and allowed the opportunity to ask questions. Minimal qualitative information exists as to how much of this material patients retain and(More)
This paper addresses nonphysical reflections encountered in the discretization of wave equations on nonuniform grids. Such nonphysical solutions are commonly attributed to spurious modes in the numerical dispersion relation. We provide an example of a discretization in which a (nonspurious) physical mode is spuriously energized at a grid nonuniformity. It(More)
Based on the thermodynamic concept of a reservoir, we investigate a computational model for interaction with unresolved degrees of freedom (a thermal bath). We assume that a finite restricted system can be modelled by a generalized canonical ensemble, described by a density which is a smooth function of the energy of the restricted system. A thermostat is(More)