We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier–Stokes equations. We have extended the existing setting developed in the last decade (see [S. Deparis, 46 (2008) 2039–2067; A. Quarteroni and G. Rozza, 23 (2007) 923–948; K. Veroy and A.T. Patera, 47 (2005) 773–788]) to more general affine and nonaffine parametrizations (such as volume-based techniques), to a simultaneous velocity-pressure error estimates and to a fully decoupled...
A new approach for computationally efficient estimation of stability factors for
parametric partial differential equations is presented. The general parametric bilinear
form of the problem is approximated by two affinely parametrized bilinear forms at
different levels of accuracy (after an empirical interpolation procedure). The successive
constraint method is applied on the coarse level to obtain a lower bound for the stability
factors, and this...
A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at different levels of accuracy (after an empirical interpolation procedure). The successive constraint method is applied on the coarse level to obtain a lower bound for the stability factors, and this bound is extended to the fine level by adding a proper...
A new approach for computationally efficient estimation of stability factors for
parametric partial differential equations is presented. The general parametric bilinear
form of the problem is approximated by two affinely parametrized bilinear forms at
different levels of accuracy (after an empirical interpolation procedure). The successive
constraint method is applied on the coarse level to obtain a lower bound for the stability
factors, and this...
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...
The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affine parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions....
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