Publications by Gianluigi Rozza

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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 propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric config ...

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

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 ...

Reduced basis approximations for geometrically parametrized advection- diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized ...

Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this ...

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 ...

The stochastic collocation method has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method, primarily developed for solving parametric systems, has been recently used to deal with ...

Gianluigi Rozza

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Real-time reduced basis solutions for Navier-Stokes equations: optimization of parametrized bypass configurations

Model reduction of semiaffinely parameterized partial differential equations by two-level affine approximation

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Shape design in aorto-coronaric bypass anastomoses using perturbation theory

Reduced basis approximation for shape optimization in thermal flows with a parametrized polynomial geometric map

Reduced basis methods for optimal control of advection-diffusion problems

Computing upper and lower bounds for linear outputs of elasticity by the smoothed finite element method

A mathematical approach in the design of arterial bypass using unsteady Stokes equations

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Real time reduced basis techniques for arterial bypass geometries

Matematica in volo con Solar Impulse