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Piecewise Constant (piecewise + constant)

Distribution by Scientific Domains

Engineering	80%

Selected Abstracts

Positive-definite q -families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
Michael G. Edwards
Abstract A new family of locally conservative cell-centred flux-continuous schemes is presented for solving the porous media general-tensor pressure equation. A general geometry-permeability tensor approximation is introduced that is piecewise constant over the subcells of the control volumes and ensures that the local discrete general tensor is elliptic. A family of control-volume distributed subcell flux-continuous schemes are defined in terms of the quadrature parametrization q (Multigrid Methods. Birkhauser: Basel, 1993; Proceedings of the 4th European Conference on the Mathematics of Oil Recovery, Norway, June 1994; Comput. Geosci. 1998; 2:259,290), where the local position of flux continuity defines the quadrature point and each particular scheme. The subcell tensor approximation ensures that a symmetric positive-definite (SPD) discretization matrix is obtained for the base member (q=1) of the formulation. The physical-space schemes are shown to be non-symmetric for general quadrilateral cells. Conditions for discrete ellipticity of the non-symmetric schemes are derived with respect to the local symmetric part of the tensor. The relationship with the mixed finite element method is given for both the physical-space and subcell-space q -families of schemes. M -matrix monotonicity conditions for these schemes are summarized. A numerical convergence study of the schemes shows that while the physical-space schemes are the most accurate, the subcell tensor approximation reduces solution errors when compared with earlier cell-wise constant tensor schemes and that subcell tensor approximation using the control-volume face geometry yields the best SPD scheme results. A particular quadrature point is found to improve numerical convergence of the subcell schemes for the cases tested. Copyright © 2007 John Wiley & Sons, Ltd. [source]

dsoa: The implementation of a dynamic system optimization algorithm

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2010
Brian C. Fabien
Abstract This paper describes the ANSI C/C++ computer program dsoa, which implements an algorithm for the approximate solution of dynamics system optimization problems. The algorithm is a direct method that can be applied to the optimization of dynamic systems described by index-1 differential-algebraic equations (DAEs). The types of problems considered include optimal control problems and parameter identification problems. The numerical techniques are employed to transform the dynamic system optimization problem into a parameter optimization problem by: (i) parameterizing the control input as piecewise constant on a fixed mesh, and (ii) approximating the DAEs using a linearly implicit Runge-Kutta method. The resultant nonlinear programming (NLP) problem is solved via a sequential quadratic programming technique. The program dsoa is evaluated using 83 nontrivial optimal control problems that have appeared in the literature. Here we compare the performance of the algorithm using two different NLP problem solvers, and two techniques for computing the derivatives of the functions that define the problem. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Optimal and sub-optimal control in Dengue epidemics

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2001
Marco Antonio Leonel Caetano
Abstract This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright © 2001 John Wiley & Sons, Ltd. [source]

CONTROLLABILITY OF A CLASS OF SINGULAR SYSTEMS

ASIAN JOURNAL OF CONTROL, Issue 4 2006
Guangming Xie
ABSTRACT In this paper, several different concepts of controllability are investigated for a class of linear singular systems which system parameters are piecewise constant. Necessary and sufficient geometric criteria for C-controllability and R-controllability of such systems are established, respectively. These conditions can be easily transformed into algebraic form. By applying the principle of duality, C-observability is discussed as well. Furthermore, the intrinsic relationship between these results and existing results are also discussed. Then, a novel necessary, and sufficient criterion for C-controllability of linear time-invariant singular systems is derived as a byproduct. [source]

Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models

BIOMETRICS, Issue 4 2003
Wenqing He
Summary. This article presents methodology for multivariate proportional hazards (PH) regression models. The methods employ flexible piecewise constant or spline specifications for baseline hazard functions in either marginal or conditional PH models, along with assumptions about the association among lifetimes. Because the models are parametric, ordinary maximum likelihood can be applied; it is able to deal easily with such data features as interval censoring or sequentially observed lifetimes, unlike existing semiparametric methods. A bivariate Clayton model (1978, Biometrika65, 141,151) is used to illustrate the approach taken. Because a parametric assumption about association is made, efficiency and robustness comparisons are made between estimation based on the bivariate Clayton model and "working independence" methods that specify only marginal distributions for each lifetime variable. [source]