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We apply the reduced basis method to solve Navier-Stokes equations in parametrized domains. Special attention is devoted to the treatment of the parametrized nonlinear transport term in the reduced basis framework, including the case of nonaffine parametri ...
We present an approach to the construction of lower bounds for the coercivity and inf–sup stability constants required in a posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. The method, based ...
We present an application of reduced basis method for Stokes equations in domains with affine parametric dependence. The essential components of the method are (i) the rapid convergence of global reduced basis approximations – Galerkin projection onto a sp ...
Multi-level geometrical approaches in the study of aorto-coronaric bypass anastomoses configurations are discussed. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the incoming branch of the bypass (t ...
The text is focused on formulation, analysis, and computational procedures for reduced basis approximation and a posteriori error estimation for parametrized PDEs in the real-time and many-query contexts. The book also serves as background and (certain spe ...
(C) MIT, Massachusetts Institute of Technology2007
In this paper we present an approach for the study of aorto-coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the ...
We present an application in multi-parametrized sub-domains based on a technique for the rapid and reliable prediction of linear-functional outputs of elliptic coercive partial differential equations with affine parameter dependence (reduced-basis methods) ...
The reduced basis method on parametrized domains is applied to approximate blood flow through an arterial bypass. The aim is to provide (a) a sensitivity analysis for relevant geometrical quantities of interest in bypass configurations and (b) rapid and re ...
We present a new approach in the study of aorto-coronaric bypass anastomoses configurations based on small perturbation theory. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming ...
Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of the Galerkin-Finite Element (FE) method, we adopt a novel a poste ...