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In this paper, we continue the work on implicit–explicit (IMEX) time discretizations for the incompressible Oseen's equations that we started in Burman et al. [Implicit–explicit time discretization for Oseen's equation at high Reynolds number with application to fractional step methods, SIAM J. Numer. Anal.61 (2023) 2859–2886]. The pressure velocity coupling and the viscous terms are treated implicitly, while the convection term is treated explicitly using extrapolation. Herein, we focus on the IMEX Crank–Nicolson method for time discretization. For the discretization in space we consider finite element methods with stabilization on the gradient jumps. The stabilizing terms ensure inf–sup stability for equal order interpolation and robustness at high Reynolds number. Under suitable Courant conditions, we prove the stability of the IMEX Crank–Nicolson scheme in this regime. The stabilization allows us to prove error estimates of order O (h k + 1 2 + τ 2). Here h is the mesh parameter, k the polynomial order and τ the time step. Finally, we discuss some fractional step methods that are implied by the IMEX scheme. Numerical examples are reported comparing the different methods when applied to the Navier–Stokes' equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel vertexing algorithm for determining the point of primary interaction, based on the linear extrapolation of tracks in the vicinity of the beamline. The algorithm considers tracks as infinitely elongated ellipsoids, thereby reducing the track vertexing problem to a vertex-to-points proximity problem. We have implemented the concept in C++ with the aid of our previously reported NXV4 package three for vectors and matrices, which gives very good CPU performance. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce a class of mixed-norm Herz spaces, Ė q → α → , p → (ℝ n) , which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on Ė q → α → , p → (ℝ n). Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on Ė q → α → , p → (ℝ n). As applications, the authors develop various real-variable theory of Hardy spaces associated with Ė q → α → , p → (ℝ n) by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of Ė q → α → , p → (ℝ n) and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem. [ABSTRACT FROM AUTHOR]

Real-time hybrid simulation (RTHS) is recently applied to study the vibration of the vehicle–bridge coupling system, where bridges and the vehicle are the numerical and experimental substructures respectively. Inevitable time delay of the boundary loading imposed to the experimental substructure will greatly affect the accuracy and stability of RTHS. To minimize the time delay effects, this paper proposes a recursive prediction optimal (RPO) compensator based on optimal control and recursive least squares. The numerical simulation of the RTHS of the vehicle–bridge coupling system is conducted using MATLAB/Simulink. The performance of the RPO method is compared with three traditional time delay compensation methods (i.e. the polynomial extrapolation (NI), the inverse compensation (IC) and the derivative feedforward (DF)) through both open-loop and RTHS simulations. The RPO method shows the best compensation performance in the frequency range up to 20 Hz. [ABSTRACT FROM AUTHOR]

We construct and analyze a second-order parameter uniform numerical method for parabolic singularly perturbed space-delay problems with interior turning point. The considered problem's solution possesses an interior layer in addition to twin boundary layers due to the presence of delay. Some theoretical estimates on derivatives of the analytical solution, which are useful for conducting the error analysis, are given. The proposed technique employs an upwind scheme on a fitted Bakhvalov–Shishkin mesh in the spatial variable and implicit-Euler scheme on a uniform mesh in the time variable. This discretization of the problem is shown to be uniformly convergent of O (Δ τ + − 1) , where Δ τ is the step size in the temporal direction and K denotes the number of mesh-intervals in the spatial direction. Further, to improve the accuracy, we make use of Richardson extrapolation and establish parameter-uniform convergence of O ((Δ τ) 2 + − 2) for the resulting scheme. Numerical experiments are performed over two test problems for validation of the theoretical predictions. [ABSTRACT FROM AUTHOR]

In industrial applications it is quite common to use stochastic-volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local-volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small-time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration. [ABSTRACT FROM AUTHOR]

Sensitivity analysis is a powerful tool for analyzing multi-parameter models. For example, the Fisher information matrix (FIM) and the Cramér–Rao bound (CRB) involve derivatives of a forward model with respect to parameters. However, these derivatives are difficult to estimate in ocean acoustic models. This work presents a frequency-agnostic methodology for accurately estimating numerical derivatives using physics-based parameter preconditioning and Richardson extrapolation. The methodology is validated on a case study of transmission loss in the 50–400 Hz band from a range-independent normal mode model for parameters of the sediment. Results demonstrate the utility of this methodology for obtaining Cramér–Rao bound (CRB) related to both model sensitivities and parameter uncertainties, which reveal parameter correlation in the model. This methodology is a general tool that can inform model selection and experimental design for inverse problems in different applications. [ABSTRACT FROM AUTHOR]

Quantitative technology forecasting uses quantitative methods to understand and project technological changes. It is a broad field encompassing many different techniques and has been applied to a vast range of technologies. A widely used approach in this field is trend extrapolation. Based on the literature available to us, there has been little or no attempt made to systematically review the empirical evidence on quantitative trend extrapolation techniques. This study attempts to close this gap by conducting a systematic review of the technology forecasting literature addressing the application of quantitative trend extrapolation techniques. We identified 25 studies relevant to the objective of this research and classified the techniques used in the studies into different categories, among which the growth curves and time series methods were shown to remain popular over the past decade while the newer methods, such as machine learning-based hybrid models, have emerged in recent years. As more effort and evidence are needed to determine if hybrid models are superior to traditional methods, we expect a growing trend in the development and application of hybrid models to technology forecasting. [ABSTRACT FROM AUTHOR]