Publications by Gianluigi Rozza

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This work focuses on the approximation of parametric steady Navier-- Stokes equations by the reduced basis method. For a particular instance of the parameters under consideration, we are able to solve the underlying partial differential equations, compute ...

This paper focuses on the parametric study of steady and unsteady forced and natural convection problems by the certified reduced basis method. These problems are characterized by an input-output relationship in which given an input parameter vector — mate ...

In this paper we further develop an approach previously introduced in [Lassila and Rozza, C.M.A.M.E 2010] for shape optimization that combines a suitable low-dimensional parametrization of the geometry (yielding a geometrical reduction) with reduced basis ...

Reduced Basis (RB) method has successfully been used in 2D to solve heat transfer parametrized problems. In this work, we present some 3D applications in the same field. We consider two problems, the steady Thermal Fin and the time dependent Graetz Flow, w ...

In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...

In this paper we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the compu ...

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection led and consider a stochas ...

We present a new model reduction technique for steady fluid-structure interaction problems. When the fluid domain deformation is suitably parametrized, the coupling conditions between the fluid and structure can be formulated in the low-dimensional space o ...

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 diff ...

This paper extends the reduced basis method for the solution of parametrized optimal control problems presented in Negri et al. (2013) to the case of noncoercive (elliptic) equations, such as the Stokes equations. We discuss both the theoretical properties ...

This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular system based on stochastic simulation of a one dimensional arterial network. A general analysis of different uncertainties and probability characteriza ...

Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods, in scientic computing may become crucial in applications of increasing complexity. In this paper we review the reduced basis method (built upon a high-delity "truth" f ...

We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...

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 ...

We provide an introduction on reduced basis (RB) method for the solution of parameterized partial differential equations (PDEs). We introduce all the main ingredients to describe the methodology and the algorithms used to build the approximation spaces and ...

In this work we present a stable proper orthogonal decomposition (POD)-Galerkin approximation for parametrized steady incompressible Navier-Stokes equations with low Reynolds number. Supremizers solutions are added to the reduced velocity space in order to ...

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...

In this paper we discuss the application of the certified reduced basis method and the associated software package rbMIT (c) to ``worked problems'' in steady and unsteady conduction. Each worked problem is characterized by an input parameter vector --- mat ...

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...

In this work, we propose viable and efficient strategies for the stabilization of the reduced basis approximation of an advection dominated problem. In particular, we investigate the combination of a classic stabilization method (SUPG) with the Offline-Onl ...

Gianluigi Rozza

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Reduced basis method for multi-parameter dependent steady Navier-Stokes equations: applications to natural convection in a cavity

Reduced Basis Methods and A Posteriori Error Estimators for Heat Transfer Problems

Shape optimization for viscous flows by reduced basis methods and free-form deformation

Comparison and combination of reduced order modelling techniques in 3D parametrized heat transfer problems

A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks

Model reduction techniques for fast blood flow simulation in parametrized geometries

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

A reduced basis model with parametric coupling for fluid-structure interaction problems

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations

Simulation-based uncertainty quantification of human arterial network hemodynamics

Certified Reduced Basis Approximation for Parametrized Partial Differential Equations and Applications

A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices

On optimization, control and shape design of an arterial bypass

An introduction to reduced basis method for parametrized PDEs

Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations

Computational Reduction for Parametrized PDEs: Strategies and Applications

Real-Time Reliable Simulation of Heat Transfer Phenomena

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

Stabilized reduced basis method for parametrized advection-diffusion PDEs