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.

Locking-free finite element methods for shells

Abstract: We propose a new family of finite element methods for the Naghdi shell model, one method associated with each nonnegative integer k. The methods are based on a nonstandard mixed formulation, and the kth method employs triangular Lagrange finite elements of degree k+2 augmented by bubble functions of degree k + 3 for both the displacement and rotation variables, and discontinuous piecewise polynomials of degree k for the shear and membrane stresses. This method can be implemented in terms of the displacement and rotation variables alone; as the minimization of an altered energy functional over the space mentioned. The alteration consists of the introduction of a weighted local projection into part, but not all, of the shear and membrane energy terms of the usual Naghdi energy. The relative error in the method, measured in a norm which combines the H I norm of the displacement and ro tation fields and an appropriate norm of the shear and membrane stress fields, converges to zero with order k+1 uniformly with respect to the shell thickness for smooth solutions, at least under the assumption that certain geometrical coefficients in the Nagdhi model are replaced by piecewise constants.

A unified treatment of thick and thin film elastohydrodynamic problems by using higher order element methods

Abstract: A unified mathematical treatment of thick and thin film elastohydrodynamic lubrication problems is presented. The construction of approximate solutions is discussed by using Ritz-Galerkin methods with piecewise polynomial basis functions. In particular for the line contact problem, smooth Hermite and cubic spline spaces are used to obtain solutions over a wide load-speed range. Pressure ‘spikes’ are obtained.

Neighboring Optimal Aircraft Guidance in Winds

Abstract: The technique of Neighboring Optimal Control is extended to handle cases of parameter change in the system dynamic model. This extension is used to develop an algorithm for optimizing horizontal aircraft trajectories in general wind fields using time-varying linear feedback gains. The minimum-time problem for an airplane traveling horizontally between two points in a variable wind field (a type of Zermelo Problem) is used to illustrate how perturbations in system parameters can be accounted for by augmenting the dynamic model with additional bias states. For the special case of a constant wind shear in the cross-track direction, analytical and numerical results are derived for bias perturbations. Numerical simulations are presented to demonstrate the performance of the proposed state-augmentation technique. An additional example is used to demonstrate an algorithm to compute near-optimal trajectories in general wind fields. The algorithm is based on nondimensionalizing the neighboring optimal control solutions and using piecewise linearly varying wind and horizontal wind shear parameters. One proposed application of this technique is to the computation and real-time update of time-optimal trajectories in wind fields by onboard flight management systems and by ground-based air traffic management automation tools.

Narrowest‐over‐threshold detection of multiple change points and change‐point‐like features

Abstract: We propose a new, generic and flexible methodology for non-parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.

Tensor voting for image correction by global and local intensity alignment

Abstract: This work presents a voting method to perform image correction by global and local intensity alignment. The key to our modeless approach is the estimation of global and local replacement functions by reducing the complex estimation problem to the robust 2D tensor voting in the corresponding voting spaces. No complicated model for replacement function (curve) is assumed. Subject to the monotonic constraint only, we vote for an optimal replacement function by propagating the curve smoothness constraint using a dense tensor field. Our method effectively infers missing curve segments and rejects image outliers. Applications using our tensor voting approach are proposed and described. The first application consists of image mosaicking of static scenes, where the voted replacement functions are used in our iterative registration algorithm for computing the best warping matrix. In the presence of occlusion, our replacement function can be employed to construct a visually acceptable mosaic by detecting occlusion which has large and piecewise constant color. Furthermore, by the simultaneous consideration of color matches and spatial constraints in the voting space, we perform image intensity compensation and high contrast image correction using our voting framework, when only two defective input images are given.