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Bellman approach to some problems in harmonic analysis

Alexander Volberg (2001/2002)

Séminaire Équations aux dérivées partielles

The stochastic optimal control uses the differential equation of Bellman and its solution - the Bellman function. Recently the Bellman function proved to be an efficient tool for solving some (sometimes old) problems in harmonic analysis.

Bilevel Approach of a Decomposed Topology Optimization Problem

A. Makrizi, B. Radi (2010)

Mathematical Modelling of Natural Phenomena

In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed...

Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes...

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