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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
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Journal ArticleDOI
TL;DR: In this paper, a faster implicitly decoupled differential/algebraic equation (DAE) integration technique for post-fault power system dynamics for prediction use is presented.
Abstract: Using new systems capable of making synchronized phasor measurements, the real-time stability assessment of a transient event in power systems has become an important area of investigation. Using these phasor measurements as input conditions for computing a relatively good, simplified dynamic model can yield accurate and real-time transient stability prediction in a central location equipped with high-speed computers. In an effort to reduce the computing time for integrating the differential/algebraic equation (DAE) model of postfault power system dynamics for prediction use, this paper presents a faster implicitly decoupled PQ integration technique. Two piecewise dynamic equivalents are also proposed, i.e., piecewise constant current load equivalent and piecewise constant transfer admittance equivalent. These equivalents can eliminate the algebraic equations by approximating the load flow solution piecewisely such that only internal generator buses are preserved, while approximately retaining the characteristics of the nonlinear loads. The proposed techniques have been tested on two sample power systems with promising simulation results.

91 citations

Journal ArticleDOI
TL;DR: In this paper, the application of the Kirchhoff transformation to the thermal analysis of semiconductor devices with temperature-dependent and piecewise inhomogeneous thermal conductivity is discussed. But the authors do not consider the case where the ratio of thermal conductivities is temperature independent, unless the apparent temperature is continuous.
Abstract: The paper presents a discussion on the application of the Kirchhoff transformation to the thermal analysis of semiconductor devices with temperature-dependent and piecewise inhomogeneous thermal conductivity. The Kirchhoff transformation is shown to generally reduce the problem to the solution of the linear heat equation with nonlinear jump conditions on the apparent temperature across subdomains, unless the ratio of the thermal conductivities is temperature independent, in which case the apparent temperature is continuous. In many practical cases, the temperature dependence of the thermal conductivity can be approximated in all subdomains so as to enforce this condition; one and two-dimensional examples are discussed to show that in realistic configurations (devices with metal heat sinks, multilayered structures made of different semiconductors) the error thereby introduced is acceptably low.

91 citations

Journal ArticleDOI
TL;DR: A reliable and efficient residual-based a posteriori error estimator for the coupling of fluid flow with porous media flow is derived and can be extended to other finite element subspaces yielding a stable Galerkin scheme.
Abstract: In this paper we develop an a posteriori error analysis of a new conforming mixed finite element method for the coupling of fluid flow with porous media flow. The flows are governed by the Stokes and Darcy equations, respectively, and the transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The finite element subspaces consider Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for a Lagrange multiplier defined on the interface. We derive a reliable and efficient residual-based a posteriori error estimator for this coupled problem. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, and local approximation properties of the Clement interpolant and Raviart-Thomas operator. On the other hand, Helmholtz decomposition, inverse inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.

90 citations

Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of finding a finite element approximation to the solution of a linear elliptic boundary value problem on a square, and established an approximation in a function space consisting of tensor products of piecewise polynomials of degree not greater than r.
Abstract: Collocation at Gaussian quadrature points as a means of determining a $C^1 $ finite element approximation to the solution of a linear elliptic boundary value problem on a square is studied. Optimal order $L^2 $ and $H^1 $ error estimates are established for approximation in a function space consisting of tensorproducts of $C^1 $ piecewise polynomials of degree not greater that r, where $r \geqq 3$.

90 citations

Journal ArticleDOI
TL;DR: In this article, the convergence to equilibrium in terms of Wasserstein distance has been studied for piecewise deterministic Markov processes with two components, where the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component.
Abstract: We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second component is discrete and its jump rates may depend on the position of the whole process. Under regularity assumptions on the jump rates and Wasserstein contraction conditions for the underlying dynamics, we provide a concrete criterion for the convergence to equilibrium in terms of Wasserstein distance. The proof is based on a coupling argument and a weak form of the Harris theorem. In particular, we obtain exponential ergodicity in situations which do not verify any hypoellipticity assumption, but are not uniformly contracting either. We also obtain a bound in total variation distance under a suitable regularising assumption. Some examples are given to illustrate our result, including a class of piecewise deterministic Markov processes.

90 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
2023917
20222,014
20211,089
20201,147
20191,106