429 research outputs found
Polyhedral Analysis using Parametric Objectives
The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output
Entropic lattice Boltzmann methods
We present a general methodology for constructing lattice Boltzmann models of
hydrodynamics with certain desired features of statistical physics and kinetic
theory. We show how a methodology of linear programming theory, known as
Fourier-Motzkin elimination, provides an important tool for visualizing the
state space of lattice Boltzmann algorithms that conserve a given set of
moments of the distribution function. We show how such models can be endowed
with a Lyapunov functional, analogous to Boltzmann's H, resulting in
unconditional numerical stability. Using the Chapman-Enskog analysis and
numerical simulation, we demonstrate that such entropically stabilized lattice
Boltzmann algorithms, while fully explicit and perfectly conservative, may
achieve remarkably low values for transport coefficients, such as viscosity.
Indeed, the lowest such attainable values are limited only by considerations of
accuracy, rather than stability. The method thus holds promise for
high-Reynolds number simulations of the Navier-Stokes equations.Comment: 54 pages, 16 figures. Proc. R. Soc. London A (in press
Complexity Results for Fourier-Motzkin Elimination
In this thesis, we propose a new method for removing all the redundant inequalities generated by Fourier-Motzkin elimination. This method is based on Kohler’s work and an improved version of Balas’ work. Moreover, this method only uses arithmetic operations on matrices. Algebraic complexity estimates and experimental results show that our method outperforms alternative approaches based on linear programming
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