Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: A robust technique for directly parametrizing a surface by cutting it into charts and mapping these piecewise onto a planar domain is introduced.
Abstract: The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a g...
186 citations
TL;DR: In this article, it was shown that if the time-periodic coefficients in the delayed Mathieu equation are approximated by piecewise constant functions, then there is no need to use higher than first-order approximations of the delayed term.
184 citations
TL;DR: A modification of the typical minimum-structure inver-sion algorithm is presented that generates blocky, piecewise-constant earth models that are often more consistent with the authors' real or perceived knowledge of the subsurface than the fuzzy, smeared-out models produced by current minimum-Structure inversions.
Abstract: A modification of the typical minimum-structure inver-sion algorithm is presented that generates blocky, piecewise-constant earth models. Such models are often more consistent with our real or perceived knowledge of the subsurface than the fuzzy, smeared-out models produced by current minimum-structure inversions. The modified algorithm uses l1 -type measures in the measure of model structure instead of the traditional sum-of-squares, or l2 , measure. An iteratively reweighted least-squares procedure is used to deal with the nonlinearity introduced by the non- l2 measure. Also, and of note here, diagonal finite differences are included in the measure of model structure. This enables dipping interfaces to be formed. The modified algorithm retains the benefits of the minimum-structure style of inversion — namely, reliability, robustness, and minimal artifacts in the constructed model. Two examples are given: the 2D inversion of synthetic magnetotelluric data and the 3D inversion of gravity data from the Ovo...
184 citations
TL;DR: In this article, a discrete analogue of continuous time ratio-dependent predator-prey system is proposed, which is governed by nonautonomous difference equations, modeling the dynamics of the prey and the predator having nonoverlapping generations.
184 citations
TL;DR: In this article, an extension of the piecewise parabolic method to special relativistic fluid dynamics in multidimensions is presented, which can be used for computations in non-Cartesian geometries.
Abstract: We present an extension of the piecewise parabolic method to special relativistic fluid dynamics in multidimensions. The scheme is conservative, dimensionally unsplit, and suitable for a general equation of state. Temporal evolution is second-order accurate and employs characteristic projection operators; spatial interpolation is piecewise parabolic making the scheme third-order accurate in smooth regions of the flow away from discontinuities. The algorithm is written for a general system of orthogonal curvilinear coordinates and can be used for computations in non-Cartesian geometries. A nonlinear iterative Riemann solver based on the two-shock approximation is used in flux calculation. In this approximation, an initial discontinuity decays into a set of discontinuous waves only implying that, in particular, rarefaction waves are treated as flow discontinuities. We also present a new and simple equation of state that approximates the exact result for the relativistic perfect gas with high accuracy. The strength of the new method is demonstrated in a series of numerical tests and more complex simulations in one, two, and three dimensions.
183 citations