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Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of coercive elliptic partial differential equations with affine (input) parameter dependence. The critical ingredients are: reduced-basis approximation to effect significant reduction in state-space dimensionality; a posteriori error bounds to provide rigorous error estimation and control; “offline/online” computational decompositions to permit rapid evaluation of output bounds, output bound gradients, and output bound Hessians in the limit of many queries; and reformulation of the approximate optimization statement to ensure (true) feasibility and control of suboptimality. To illustrate the method we consider the design of a three-dimensional thermal fin: Given volume and power objective-function weights, and root temperature “not-to-exceed” limits, the optimal geometry and heat transfer coefficient can be determined—with guaranteed feasibility—in only 2.3 seconds on a 500 MHz Pentium machine; note the latter includes only the online component of the calculations. Our method permits not only interactive optimal design at conception and manufacturing, but also real-time reliable adaptive optimal design in operation.
Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
We present a technique for the rapid and reliable optimization of systems characterized by linear-functional outputs of coercive elliptic partial differential equations with affine (input) parameter dependence. The critical ingredients are: reduced-basis approximation to effect significant reduction in state-space dimensionality; a posteriori error bounds to provide rigorous error estimation and control; “offline/online” computational decompositions to permit rapid evaluation of output bounds, output bound gradients, and output bound Hessians in the limit of many queries; and reformulation of the approximate optimization statement to ensure (true) feasibility and control of suboptimality. To illustrate the method we consider the design of a three-dimensional thermal fin: Given volume and power objective-function weights, and root temperature “not-to-exceed” limits, the optimal geometry and heat transfer coefficient can be determined—with guaranteed feasibility—in only 2.3 seconds on a 500 MHz Pentium machine; note the latter includes only the online component of the calculations. Our method permits not only interactive optimal design at conception and manufacturing, but also real-time reliable adaptive optimal design in operation.
Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
Optim Eng
Oliveira, I. B. (author) / Patera, A. T. (author)
Optimization and Engineering ; 8 ; 43-65
2007-03-01
23 pages
Article (Journal)
Electronic Resource
English
Engineering optimization , Reduced-basis approximation , <italic>A posteriori</italic> error estimation , Output bounds , Uncertainty control , Parametrized partial differential equations , Real-time computing Mathematics , Optimization , Engineering, general , Systems Theory, Control , Environmental Management , Operations Research/Decision Theory , Financial Engineering , Mathematics and Statistics
A class of affinely equivalent Voronoi parallelohedra
| British Library Online Contents | 2014