Higher‐order extensions of a discontinuous Galerkin method for mid‐frequency Helmholtz problems

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of Helmholtz problems in the mid‐frequency regime. In this paper, this method is extended to higher‐order elements. Performance results obtained for various two‐dimensional problems highlight the advantages of these elements over classical higher‐order Galerkin elements such as Q₂ and Q₄ for the discretization of interior and exterior Helmholtz problems. Copyright © 2004 John Wiley & Sons, Ltd.     

A Lagrange duality characterisation for stability under arbitrary switching in switched positive linear systems

The present communication is concerned with uniform exponential stability, under arbitrary switching, in discrete-time switched positive linear systems. Lagrange duality is used in order to obtain a new characterisation for uniform exponential stability which is in terms of sets of inequalities involving each of the matrices that represent the modes of the system. These sets of inequalities are shown to generalise the classical linear Lyapunov inequality that characterises, in positive matrices, the property of being Schur. Each solution to these sets of inequalities is shown to provide a representation, in terms of a number of linear functionals, for a common Lyapunov function for the switched positive linear system. A result is further presented which conveys to, a conservative upper bound on the minimum required number of linear functionals (in the above mentioned representation), and also to a method for computing them. Our proof for the aforementioned characterisation is based on another (equivalent) characterisation, in terms of the solvability of a dynamic programming equation associated to the switched positive linear system, which is also reported in the paper. In particular, it is shown that the associated dynamic programming equation has at most one solution. And this solution is shown to be convex, monotonic, positively homogeneous, and it yields a common Lyapunov function for the switched positive linear system.     

Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods

We investigate various strategies to enforce the kinematics at an embedded interface for transient problems within the extended finite element method. In particular, we focus on explicit time integration of the semi‐discrete equations of motion and extend both dual and primal variational frameworks for constraint enforcement to a transient regime. We reiterate the incompatibility of the dual formulation with purely explicit time integration and the severe restrictions placed by the Courant–Friedrichs–Levy condition on primal formulations. We propose an alternate, consistent formulation for the primal method and derive an estimate for the stabilization parameter, which is more amenable in an explicit dynamics framework. Importantly, the use of the new estimate circumvents the need for any tolerances as an interface approaches an element boundary. We also show that with interfacial constraints, existing mass lumping schemes can lead to prohibitively small critical time steps. Accordingly, we propose a mass lumping procedure, which provides a more favorable estimate. These techniques are then demonstrated on several benchmark numerical examples, where we compare and contrast the accuracy of the primal methods against the dual methods in enforcing the constraints. Copyright © 2012 John Wiley & Sons, Ltd.     

PID position regulation in one-degree-of-freedom Euler–Lagrange systems actuated by a PMSM

This paper is concerned with position regulation in one-degree-of-freedom Euler–Lagrange Systems. We consider that the mechanical subsystem is actuated by a permanent magnet synchronous motor (PMSM). Our proposal consists of a Proportional-Integral-Derivative (PID) controller for the mechanical subsystem and a slight variation of field oriented control for the PMSM. We take into account the motor electric dynamics during the stability analysis. We present, for the first time, a global asymptotic stability proof for such a control scheme without requiring the mechanical subsystem to naturally possess viscous friction. Finally, as a corollary of our main result we prove global asymptotic stability for output feedback PID regulation of one-degree-of-freedom Euler–Lagrange systems when generated torque is considered as the system input, i.e. when the electric dynamics of PMSM's is not taken into account.     

A PRACTICAL APPLICATION OF A NUMERICAL OPTIMIZATION TECHNIQUE IN THE FEEDMILL INDUSTRY

The cow model of Meijer describes a mathematical relation between the predicted daily milk production and the corresponding feed intake needed for lactating cows. The milk production is a function of several parameters defined for each cow. Used in least cost calculations of daily rations, an optimization problem is obtained, which consists of one highly non-linear equality constraint, together with several linear inequality constraints. Their number required in the optimization can vary and depends on the user's choice. The cost function itself gives a linear relation between the prices of the different forages mixed in the optimal blend. The optimization result has been implemented with the aid of Augmented Lagrange Functions with a view to apply the program in the feedmill industry.     

Sage of Lacock

Abstract

‘The good is oft interred with their bones.’ Much of what has been written of William Henry Fox Talbot has done him meagre justice: criticism for patenting his inventions, accusations that he patented the ideas of others, denigration of the importance of his discoveries. Though acknowledged as a scientist, his place as an artistic worker in the medium he invented has not been appreciated.     

岩土工程可靠度分析的拉格朗日乘数法

基于可靠指标标准正态空间计算的数学模型,运用拉格朗日乘数法,提出了计算岩土工程设计验算点和可靠指标的方法.该方法适用于任何概率分布的相关变量,不必计算当量正态均值和方差、相关变量独立变换,也适用于功能函数为高度线性时采用JC法计算可靠指标迭代不能收敛的情况.通过建立构造函数,然后求其对各个变量的一阶偏导并与结构的功能函数联立求解出验算点坐标,之后求出可靠性指标.由于标准正态分布函数的反函数表达式不能给出,在求解其导数时可使用有理多项式法求解.通过二个算例分析表明该方法简单、可靠和有效,值得在工程实践中推广.     

An image pixel based variational model for histogram equalization

In this paper, we develop an image pixel based histogram equalization model for image contrast enhancement. The approach is to propose a variational model containing an energy functional to adjust the pixel values of an input image directly so that the resulting histogram can be redistributed to be uniform. This idea is different from existing histogram equalization algorithms where a histogram based on the input image is constructed, a mapping is determined to output a uniform histogram and then the pixel values of the input image are adjusted based on the mapping. In the variational model, a mean brightness term is incorporated to preserve the brightness of the input image, and a geometry constraint can also be added to keep the geometry structure of the input image. Theoretically, the existence of the minimizer of the proposed model, and the convergence of the proposed algorithm are given. Experimental results are reported to demonstrate that the performance of the proposed model are competitive with the other testing histogram equalization methods for several testing images.     

A 3D multi-grid algorithm for the Chan–Vese model of variational image segmentation

Variational segmentation models provide effective tools for image processing applications. Although existing models are continually refined to increase their capabilities, solution of such models is often a slow process, since fast methods are not immediately applicable to nonlinear problems. This paper presents an efficient multi-grid algorithm for solving the Chan–Vese model in three dimensions, generalizing our previous work on the topic in two dimensions, but this direct generalized method is low performance or unfeasible. So here, we first present two general smoothers for a nonlinear multi-grid method and then give our three new adaptive smoothers which can choose optimal a parameter of the smoothers automatically, also we analyse them using a local Fourier analysis and our theorem to inform how to obtain an optimal parameter and the best smoother selection. Finally, various advantages of our recommended algorithm are illustrated, using both synthetic and real images.     

Efficient solution of the diesel-engine optimal control problem by time-domain decomposition

Offline solutions of the optimal control problems relating to diesel engines provide implications for causal control strategies and serve as a tool to automate the engine calibration process. However, the numerical solution of these dynamic optimisation problems is challenging. Above all, the model evaluations are expensive, integral and local inequality constraints are present, and the time horizon to be considered is long. Generally, the continuous problem is transcribed into a nonlinear mathematical program, which has a runtime that increases superlinearly with the problem size. In the literature, the time-domain decomposition of unconstrained and control-constrained problems is proposed to alleviate this often prohibiting increase in computational time. This paper extends the decomposition approach to problems with integral inequality constraints by utilising a partially dual formulation to derive equivalence conditions. To achieve these conditions, exact and approximate iteration schemes are proposed. The time-domain decomposition is combined with an iterative mesh refinement and a parallelisation of the model evaluations, which dominate the runtime of the solution process. On a standard personal computer, an overall speedup factor of 25 is achieved for a realistically sized instance of the diesel-engine problem.