Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

On the principal eigenvalue of a Robin problem with a large parameter

Abstract: We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Smooth interpolation of a mesh of curves

Abstract: The interpolation of a mesh of curves by a smooth regularly parametrized surface with one polynomial piece per facet is studied. Not every mesh with a well-defined tangent plane at the mesh points has such an interpolant: the curvature of mesh curves emanating from mesh points with an even number of neighbors must satisfy an additional “vertex enclosure constraint.” The constraint is weaker than previous analyses in the literature suggest and thus leads to more efficient constructions. This is illustrated by an implemented algorithm for the local interpolation of a cubic curve mesh by a piecewise [bi]quarticC 1 surface. The scheme is based on an alternative sufficient constraint that forces the mesh curves to interpolate second-order data at the mesh points. Rational patches, singular parametrizations, and the splitting of patches are interpreted as techniques to enforce the vertex enclosure constraint.

On the rate of convergence to equilibrium in one-dimensional systems

Abstract: We determine the essential spectral radius of the Perron-Frobenius-operator for piecewise expanding transformations considered as an operator on the space of functions of bounded variation and relate the speed of convergence to equilibrium in such one-dimensional systems to the greatest eigenvalues of generalized Perron-Frobenius-operators of the transformations (operators which yield singular invariant measures).

GDEVS: a generalized discrete event specification for accurate modeling of dynamic systems

Abstract: Given a process whose output is a dynamic function of time, the traditional discrete event specification (DEVS) approximates the input, output, and state trajectories through piecewise constant segments, where the segments correspond to discrete time intervals that are not necessarily equal in length. For processes that defy accurate modeling through piecewise constant segments, this paper presents GDEVS, a generalized discrete event specification, wherein the trajectories are organized through piecewise polynomial segments. The utilization of arbitrary polynomial functions for segments promises higher accuracies in modeling continuous processes as discrete event abstractions. In general, discrete event systems including DEVS and GDEVS execute faster on host computers because executions occur corresponding to significant changes in the system unlike in continuous simulations where execution is on a continuous basis. GDEVS' superiority over DEVS lies in its ability to discretize a system characteristic. A key contribution of GDEVS is that it permits the development of a uniform simulation environment for hybrid, i.e. both continuous and discrete, systems. GDEVS is illustrated for a first order system and a hybrid system, with piecewise linear segments. Two representative systems have been modeled under GDEVS and executed on a simulator developed for GDEVS.