In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations...
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In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invokes also a sixth order Pade approximation for the first order derivatives, using an approximation suggested by Carpenter-Gottlieb-Abarbanel (J. Comput. Phys. 108:272-295, 1993). We also introduce the derivation of a pure streamfunction formulation for the Navier-Stokes equations in three dimensions.
An improved shooting algorithm for high-power fiber laser is proposed based on the relation of the two-end boundary laser powers. By the improved shooting algorithm, the evolutions of the pump and laser powers along t...
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An improved shooting algorithm for high-power fiber laser is proposed based on the relation of the two-end boundary laser powers. By the improved shooting algorithm, the evolutions of the pump and laser powers along the fiber position for Yb-doped and Tm-doped high-power double-clad fiber lasers with the laser scattering loss are analyzed. The results prove that the improved shooting algorithm can be efficient even if the pump power is up to kilowatt level, and the initial value can all be fast convergent as long as the initial guessed laser power is smaller than the truth value. So, this improved shooting algorithm can be used in high-power double-clad fiber lasers efficiently. (C) 2010 Elsevier B.V. All rights reserved.
A model of optimal control of underflooding of restricted areas by groundwater on the basis of the initial boundary value problem for a parabolic type quasilinear equation is considered. For the initial boundary value...
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A model of optimal control of underflooding of restricted areas by groundwater on the basis of the initial boundary value problem for a parabolic type quasilinear equation is considered. For the initial boundary value problem the maximum principle is proved, sufficient conditions of the existence and uniqueness of a generalized solution, sufficient conditions of the existence of optimal control of this system are obtained. The numerical algorithm for solving the optimal control problem is constructed and the numerical calculations for a model example are given.
In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313-303, 2001;Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809-817, 2003;Ben-Art...
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In this paper we continue the study, which was initiated in (Ben-Artzi et al. in Math. Model. Numer. Anal. 35(2):313-303, 2001;Fishelov et al. in Lecture Notes in Computer Science, vol. 2667, pp. 809-817, 2003;Ben-Artzi et al. in J. Comput. Phys. 205(2):640-664, 2005 and SIAM J. Numer. Anal. 44(5):1997-2024, 2006) of the numerical resolution of the pure streamfunction formulation of the time-dependent two-dimensional Navier-Stokes equation. Here we focus on enhancing our second-order scheme, introduced in the last three afore-mentioned articles, to fourth order accuracy. We construct fourth order approximations for the Laplacian, the biharmonic and the nonlinear convective operators. The scheme is compact (nine-point stencil) for the Laplacian and the biharmonic operators, which are both treated implicitly in the time-stepping scheme. The approximation of the convective term is compact in the no-leak boundary conditions case and is nearly compact (thirteen points stencil) in the case of general boundary conditions. However, we stress that in any case no unphysical boundary condition was applied to our scheme. numerical results demonstrate that the fourth order accuracy is actually obtained for several test-cases.
In this work, we propose a heteroscedastic method in the detection of activity patterns of electroneurographic and electromyogram signals involved in rhythmic activities of nerves and muscles, respectively. The electr...
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In this work, we propose a heteroscedastic method in the detection of activity patterns of electroneurographic and electromyogram signals involved in rhythmic activities of nerves and muscles, respectively. The electric behavior observed in such signals is characterized by phases of activity and silence. The beginning and the length of electrically active and electrically silent phases in a signal allow us to quantitatively analyze the changes and the effects on a rhythmic activity produced by experimental changes In order to distinguish between these two phases, signals are assumed to be a sample of a time-dependent, normally distributed random variable with non-constant variance, and that the determination of the variance at each point allows us to determine in which phase is the signal The parameters of the model are determined by means of an iterative process which maximizes the log-likelihood under the proposed model Moreover, we apply our method to the determination of the activity phases and silence phases in sequences of experimental and synthetic electroneurographic and electromyogram signals. The results obtained with synthetic data show that the method performs well in the determination of these activity patterns Finally, the study of particular signals simulated under a generalized autoregressive conditional heteroscedasticity model suggests the robustness of the method with respect to the assumption of independence (C) 2010 Elsevier Inc. All rights reserved.
The paper is devoted to new applications of the ideas underlying Godunov's method that was developed as early as in the 1950s for solving fluid dynamics problems. This paper deals with elastoplastic problems. Base...
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The paper is devoted to new applications of the ideas underlying Godunov's method that was developed as early as in the 1950s for solving fluid dynamics problems. This paper deals with elastoplastic problems. Based on an elastic model and its modification obtained by introducing the Maxwell viscosity, a method for modeling plastic deformations is proposed.
Lithography simulators have been playing an indispensable role in process optimization and design for manufacturability (DFM). The ever smaller feature sizes demand higher numerical accuracy and faster runtime on thes...
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Lithography simulators have been playing an indispensable role in process optimization and design for manufacturability (DFM). The ever smaller feature sizes demand higher numerical accuracy and faster runtime on these lithography simulators. Aerial image simulation is the first key step in lithography simulation, and the method using transmission cross coefficient (TCC), which is a two-dimensional integral, is the most commonly used technique for full-chip aerial image simulation. In this paper, we present a very accurate, yet efficient and extensible aerial image simulator, ELIAS. We find that the majority of the numerical error during the TCC computation is due to the discontinuous boundaries of the support of the TCC integrand. We reduce the error dramatically by using a recursive integration algorithm. Because TCC is usually computed on uniform grids, we further speed up the algorithm without increasing the errors. Given the same accuracy, our new algorithm can speed up the runtime by 100 x -1000 X. Our algorithm also provides smooth tradeoff between accuracy and runtime. It can be used to benchmark other lithography aerial simulators. In addition, ELIAS provides an open-source, flexible software framework to incorporate different lithography settings.
A two-way relay channel with independent parallel Gaussian channels between the relay and the two terminals is considered. Focusing on the decode-and-forward protocol, the second phase of the communication, in which t...
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ISBN:
(纸本)9781424480166
A two-way relay channel with independent parallel Gaussian channels between the relay and the two terminals is considered. Focusing on the decode-and-forward protocol, the second phase of the communication, in which the relay broadcasts the two messages to their respective receivers, is studied. Precisely, the problem of computing the power allocation among the parallel channels that maximizes the weighted sum rate assuming arbitrarily distributed channel inputs (such as m-QAM) is stated and shown to be convex. A numerical algorithm is provided to solve the problem for the general case and, for the particular cases of high and low power regimes, expressions for the optimal power allocation are derived in closed form.
This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. numerical examples are carried out to illustrate the performance of our approach.
This paper presents a functional approximation of the M/D/1/N built on a Taylor series approximation. numerical examples are carried out to illustrate the performance of our approach.
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