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Objective Functional (objective + functional)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Note on the determination of the ignition point in forest fires propagation using a control algorithm

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
M. Bergmann
Abstract This paper is devoted to the determination of the origin point in forest fires propagation using a control algorithm. The forest fires propagation are mathematically modelled starting from a reaction diffusion model. A volume of fluid (V.O.F.) formulation is also used to determine the fraction of the area which is burnt. After having developed the objective functional and its derivative, results from an optimization process based on the simplex method is presented. It is shown that the ignition point and the final time of the fire propagation are precisely recovered, even for a realistic, non-horizontal, terrain. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Inverse optimal design of cooling conditions for continuous quenching processes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2001
Yimin Ruan
Abstract This paper presents an inverse design methodology to obtain a required yield strength with an optimal cooling condition for the continuous quenching of precipitation hardenable sheet alloys. The yield strength of a precipitation hardenable alloy can be obtained by allowing solute to enter into solid solution at a proper temperature and rapidly cooling the alloy to hold the solute in the solid solution. An aging process may be needed for the alloy to develop the final mechanical property. The objective of the design is to optimize the quenching process so that the required yield strength can be achieved. With the inverse design method, the required yield strength is specified and the sheet thermal profile at the exit of the quenching chamber can also be specified. The conjugate gradient method is used to optimize the cooling boundary condition during quenching. The adjoint system is developed to compute the gradient of the objective functional. An aluminium sheet quenching problem is presented to demonstrate the inverse design method. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Solution to shape identification problem of unsteady heat-conduction fields

HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2003
Eiji Katamine
Abstract This paper presents a numerical analysis method for shape determination problems of unsteady heat-conduction fields in which time histories of temperature distributions on prescribed subboundaries or time histories of gradient distributions of temperature in prescribed subdomains have prescribed distributions. The square error integrals between the actual distributions and the prescribed distributions on the prescribed subboundaries or in the prescribed subdomains during the specified period of time are used as objective functionals. Reshaping is accomplished by the traction method that was proposed as a solution to shape optimization problems of domains in which boundary value problems are defined. The shape gradient functions of these shape determination problems are derived theoretically using the Lagrange multiplier method and the formulation of material derivative. The time histories of temperature distributions are evaluated using the finite-element method for a space integral and the Crank,Nicolson method for a time integral. Numerical analyses of nozzle and coolant flow passage in a wing are demonstrated to confirm the validity of this method. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 212,226, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10086 [source]

OPTIMAL HARVESTING OF A SPATIALLY EXPLICIT FISHERY MODEL

NATURAL RESOURCE MODELING, Issue 2 2009
WANDI DING
Abstract We consider an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions, and logistic population growth. We consider two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control). Existence, necessary conditions, and uniqueness for the optimal harvesting control for both cases are established. Results for maximizing the yield with Neumann (no-flux) boundary conditions are also given. The optimal control when minimizing the variation is characterized by a variational inequality instead of the usual algebraic characterization, which involves the solutions of an optimality system of nonlinear elliptic partial differential equations. Numerical examples are given to illustrate the results. [source]