Publications

Liquid crystal elastomer strips as soft crawlers

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2015

Authors: 

DeSimone, Antonio and Gidoni, Paolo and Noselli, Giovanni

In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change).

Hydraulic fracture and toughening of a brittle layer bonded to a hydrogel

Journal: 

Physical review letters

Date: 

2015

Authors: 

Lucantonio, Alessandro and Noselli, Giovanni and Trepat, Xavier and DeSimone, Antonio and Arroyo, Marino

Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues.

Poroelastic toughening in polymer gels: A theoretical and numerical study

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2016

Authors: 

Noselli, Giovanni and Lucantonio, Alessandro and McMeeking, Robert M and DeSimone, Antonio

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening.

Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites

Journal: 

Meccanica

Date: 

2017

Authors: 

Lucantonio, Alessandro and Noselli, Giovanni

Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks.

Dye-enhanced visualization of rat whiskers for behavioral studies

Journal: 

Elife

Date: 

2017

Authors: 

Rigosa, Jacopo and Lucantonio, Alessandro and Noselli, Giovanni and Fassihi, Arash and Zorzin, Erik and Manzino, Fabrizio and Pulecchi, Francesca and Diamond, Mathew E

Visualization and tracking of the facial whiskers is required in an increasing number of rodent studies. Though many approaches have been employed, only high-speed videography has proven adequate for measuring whisker motion and deformation during interaction with an object. However, whisker visualization and tracking is challenging for multiple reasons, primary among them the low contrast of the whisker against its background. Here we demonstrate a fluorescent dye method suitable for visualization of one or more rat whiskers.

Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes

Journal: 

Proceedings of the National Academy of Sciences

Date: 

2017

Authors: 

Rossi, Massimiliano and Cicconofri, Giancarlo and Beran, Alfred and Noselli, Giovanni and DeSimone, Antonio

The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis.

Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: the role of sample geometry

Journal: 

International Journal of Mechanical Sciences

Date: 

2018

Authors: 

Caruso, Noe A and Cvetkovi{\'c}, Aleksandar and Lucantonio, Alessandro and Noselli, Giovanni and DeSimone, Antonio

An elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement.

Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2018

Authors: 

Bigoni, Davide and Kirillov, Oleg N and Misseroni, Diego and Noselli, Giovanni and Tommasini, Mirko

Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pflüger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of the rod in the latter case), have attracted, and still attract, a thorough research interest. In this field, the most important issue is the validation of the model itself of follower force, a nonconservative action which was harshly criticized and never realized in practice for structures with diffused elasticity.

Smart helical structures inspired by the pellicle of euglenids

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2019

Authors: 

Noselli, Giovanni and Arroyo, Marino and DeSimone, Antonio

This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder resulting from the assembly of straight and parallel strips into a cylinder of smaller height and larger radius, in which the strips are deformed into a family of parallel helices.

Swimming Euglena respond to confinement with a behavioural change enabling effective crawling

Journal: 

Nature physics

Date: 

2019

Authors: 

Noselli, Giovanni and Beran, Alfred and Arroyo, Marino and DeSimone, Antonio

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement.

Morphable structures from unicellular organisms with active, shape-shifting envelopes: Variations on a theme by Gauss

Journal: 

International Journal of Non-Linear Mechanics

Date: 

2020

Authors: 

Cicconofri, Giancarlo and Arroyo, Marino and Noselli, Giovanni and DeSimone, Antonio

We discuss some recent results on biological and bio-inspired morphing, and use them to identify promising research directions for the future. In particular, we consider issues related to morphing at microscopic scales inspired by unicellular organisms. We focus on broad conceptual principles and, in particular, on morphing approaches based on the use of Gauss' theorema egregium (Gaussian morphing).

On polymer network rupture in gels in the limit of very slow straining or a very slow crack propagation rate

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2020

Authors: 

McMeeking, RM and Lucantonio, A and Noselli, G and Deshpande, VS

The J-integral is formulated in a direct manner for a gel consisting of a cross-linked polymer network and a mobile solvent. The form of the J-integral is given for a formulation that exploits the Helmholtz energy density of the gel and expressions are provided for it in both the unswollen reference configuration of the polymer network and in the current swollen configuration of the gel when small strains are superimposed on the swollen state.

Mechanics of axisymmetric sheets of interlocking and slidable rods

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2020

Authors: 

Riccobelli, Davide; Noselli, Giovanni; Arroyo, Marino; DeSimone, Antonio

In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. Through an asymptotic expansion, we investigate both structures that comprise a discrete number of rods and the limit case of a sheet composed by infinitely many rods.

Surface tension controls the onset of gyrification in brain organoids

Journal: 

Journal of the Mechanics and Physics of Solids

Date: 

2020

Authors: 

Riccobelli, Davide; Bevilacqua, Giulia

Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which causes a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomogeneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate.

Enhancing CFD predictions in shape design problems by model and parameter space reduction

Date: 

2020

Authors: 

Marco Tezzele and Nicola Demo and Giovanni Stabile and Andrea Mola and Gianluigi Rozza

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality.

A POD-Galerkin reduced order model of a turbulent convective buoyant flow of sodium over a backward-facing step

Date: 

2020

Authors: 

Kelbij Star and Giovanni Stabile and Gianluigi Rozza and Joris Degroote

A Finite-Volume based POD-Galerkin reduced order modeling strategy for steady-state Reynolds averaged Navier--Stokes (RANS) simulation is extended for low-Prandtl number flow. The reduced order model is based on a full order model for which the effects of buoyancy on the flow and heat transfer are characterized by varying the Richardson number. The Reynolds stresses are computed with a linear eddy viscosity model. A single gradient diffusion hypothesis, together with a local correlation for the evaluation of the turbulent Prandtl number, is used to model the turbulent heat fluxes.

POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations

Date: 

2020

Authors: 

Maria Strazzullo and Francesco Ballarin and Gianluigi Rozza

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way.

A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems

Date: 

2020

Authors: 

Nicola Demo and Marco Tezzele and Gianluigi Rozza

In this work, we present an extension of the genetic algorithm (GA) which exploits the active subspaces (AS) property to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the optimum. Thus, complex and high-dimensional functions may result intractable with the standard algorithm.

POD-Galerkin reduced order methods for combined Navier-Stokes transport equations based on a hybrid FV-FE solver

Journal: 

Computers & Mathematics with Applications

Date: 

2019

Authors: 

S. Busto and G. Stabile and G. Rozza and M.E.Vázquez-Cendónc

The purpose of this work is to introduce a novel POD-Galerkin strategy for the hybrid finite volume/finite element solver introduced in Bermúdez et al. 2014 and Busto et al. 2018. The interest is into the incompressible Navier-Stokes equations coupled with an additional transport equation. The full order model employed in this article makes use of staggered meshes. This feature will be conveyed to the reduced order model leading to the definition of reduced basis spaces in both meshes.

A reduced basis approach for PDEs on parametrized geometries based on the shifted boundary finite element method and application to a Stokes flow

Journal: 

Computer Methods in Applied Mechanics and Engineering

Date: 

2019

Authors: 

Karatzas, Efthymios N and Stabile, Giovanni and Nouveau, Leo and Scovazzi, Guglielmo and Rozza, Gianluigi

We propose a model order reduction technique integrating the Shifted Boundary Method (SBM) with a POD-Galerkin strategy. This approach allows to treat more complex parametrized domains in an efficient and straightforward way. The impact of the proposed approach is threefold.

First, problems involving parametrizations of complex geometrical shapes and/or large domain deformations can be efficiently solved at full-order by means of the SBM, an unfitted boundary method that avoids remeshing and the tedious handling of cut cells by introducing an approximate surrogate boundary.

Reduced basis approaches for parametrized bifurcation problems held by non-linear Von Kármán equations

Journal: 

Journal of Scientific Computing

Date: 

2019

Authors: 

Pichi, Federico and Rozza, Gianluigi

This work focuses on the computationally efficient detection of the buckling phenomena and bifurcation analysis of the parametric Von Kármán plate equations based on reduced order methods and spectral analysis. The computational complexity - due to the fourth order derivative terms, the non-linearity and the parameter dependence - provides an interesting benchmark to test the importance of the reduction strategies, during the construction of the bifurcation diagram by varying the parameter(s).

A Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions

Journal: 

Computer Methods in Applied Mechanics and Engineering

Date: 

2019

Authors: 

Hess, Martin and Alla, Alessandro and Quaini, Annalisa and Rozza, Gianluigi and Gunzburger, Max

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions.

A Spectral Element Reduced Basis Method in Parametric CFD

Journal: 

Inbook: Numerical Mathematics and Advanced Applications - ENUMATH 2017

Date: 

2019

Authors: 

Hess, Martin W. and Rozza, Gianluigi

We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization.

A Finite Volume approximation of the Navier-Stokes equations with nonlinear filtering stabilization

Journal: 

Computers & Fluids

Date: 

2019

Authors: 

Girfoglio, Michele and Quaini, Annalisa and Rozza, Gianluigi

We consider a Leray model with a nonlinear differential low-pass filter for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under-refined meshes. For the implementation of the model, we adopt the three-step algorithm Evolve-Filter-Relax (EFR). The Leray model has been extensively applied within a Finite Element (FE) framework. Here, we propose to combine the EFR algorithm with a computationally efficient Finite Volume (FV) method.

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

Journal: 

Communications in Computational Physics

Date: 

2019

Authors: 

Sokratia Georgaka and Giovanni Stabile and Gianluigi Rozza and Michael J. Bluck

A parametric reduced order model based on proper orthogonal decom- position with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power plants. Thermal mixing of different temperature coolants in T-junction pipes leads to tem- perature fluctuations and this could potentially cause thermal fatigue in the pipe walls.

Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation

Date: 

2019

Authors: 

Nirav Vasant Shah and Martin Hess and Gianluigi Rozza

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency.

A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries

Journal: 

Inbook: IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22--25, 2018

Date: 

2020

Authors: 

Efthymios N. Karatzas and Giovanni Stabile and Nabib Atallah and Guglielmo Scovazzi and Gianluigi Rozza

A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed.

A hybrid reduced order method for modelling turbulent heat transfer problems

Journal: 

Computers & Fluids

Date: 

2020

Authors: 

Sokratia Georgaka and Giovanni Stabile and Kelbij Star and Gianluigi Rozza and Michael J. Bluck

A parametric, hybrid reduced order model approach based on the Proper Orthogonal Decomposition with both Galerkin projection and interpolation based on Radial Basis Functions method is presented. This method is tested against a case of turbulent non-isothermal mixing in a T-junction pipe, a common ow arrangement found in nuclear reactor cooling systems. The reduced order model is derived from the 3D unsteady, incompressible Navier-Stokes equations weakly coupled with the energy equation.

Efficient Geometrical parametrization for finite-volume based reduced order methods

Journal: 

International Journal for Numerical Methods in Engineering

Date: 

2020

Authors: 

Giovanni Stabile and Matteo Zancanaro and Gianluigi Rozza

In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in the framework of finite element reduced order methods, different geometries are not mapped to a common reference domain: the method relies on basis functions defined on an average deformed configuration and makes use of the Discrete Empirical Interpolation Method (D-EIM) to handle together non-affinity of the parametrization and non-linearities.

A Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation

Journal: 

SIAM Journal on Scientific Computing

Date: 

2020

Authors: 

Pichi, Federico and Quaini, Annalisa and Rozza, Gianluigi

We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time.

Reduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature

Journal: 

International Journal of Computational Fluid Dynamics

Date: 

2020

Authors: 

Hess, Martin and Quaini, Annalisa and Rozza, Gianluigi
We consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom.

Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences

Journal: 

Inbook: ENUMATH2019 proceedings

Date: 

2020

Authors: 

Maria Strazzullo and Zakia Zainib and Francesco Ballarin and Gianluigi Rozza

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, optimal control problems require a huge computational effort in order to be solved, most of all in a physical and/or geometrical parametrized setting. Reduced order methods are a reliably suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences.

Non-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition

Journal: 

Inbook: QUIET Selected Contributions

Date: 

2020

Authors: 

Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach.

Data-driven POD-Galerkin reduced order model for turbulent flows

Journal: 

Journal of Computational Physics

Date: 

2020

Authors: 

Saddam Hijazi and Giovanni Stabile and Andrea Mola and Gianluigi Rozza

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively.

Shape optimization through proper orthogonal decomposition with interpolation and dynamic mode decomposition enhanced by active subspaces

Journal: 

Inbook: VIII International Conference on Computational Methods in Marine Engineering

Date: 

2019

Authors: 

M. Tezzele, N. Demo, G. Rozza

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic mode decomposition (DMD). The ROM proposed will be enhanced by active subspaces (AS) as a pre-processing tool that reduce the parameter space dimension and suggest better sampling of the input space. We will focus on geometrical parameters describing the perturbation of a reference bulbous bow through the free form deformation (FFD) technique.

A complete data-driven framework for the efficient solution of parametric shape design and optimisation in naval engineering problems

Journal: 

Inbook: VIII International Conference on Computational Methods in Marine Engineering

Date: 

2019

Authors: 

N. Demo, M. Tezzele, A. Mola, G. Rozza

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples of the ROM application, in the naval field, can be found in [31, 24]. Mandatory ingredient for the ROM methods is the relation between the high-fidelity solutions and the parameters.

Efficient Reduction in Shape Parameter Space Dimension for Ship Propeller Blade Design

Journal: 

Inbook: VIII International Conference on Computational Methods in Marine Engineering

Date: 

2019

Authors: 

A. Mola, M. Tezzele, M. Gadalla, F. Valdenazzi, D. Grassi, R. Padovan, G. Rozza
In this work, we present the results of a ship propeller design optimization campaign carried out in the framework of the research project PRELICA, funded by the Friuli Venezia Giulia regional government. The main idea of this work is to operate on a multidisciplinary level to identify propeller shapes that lead to reduced tip vortex-induced pressure and increased efficiency without altering the thrust. First, a specific tool for the bottom-up construction of parameterized propeller blade geometries has been developed.

BladeX: Python Blade Morphing

Journal: 

The Journal of Open Source Software, 4(34), p. pp. 1203, 2019

Date: 

2019

Authors: 

M. Gadalla, M. Tezzele, A. Mola, and G. Rozza

Marine propeller blade shape is constantly studied by engineers to obtain designs that allow for enhanced hydrodynamic performance while reducing vibrations and noise emissions. In such framework, shape parametrization and morphing algorithms are crucial elements of the numerical simulation and prototyping environment required for the evaluation of new blade geometries.

Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs

Journal: 

Uncertainty Modeling for Engineering Applications, F. Canavero (ed.), Springer International Publishing, p. pp. 27–40, 2019

Date: 

2018

Authors: 

L. Venturi, D. Torlo, F. Ballarin, and G. Rozza

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process.

Computational methods in cardiovascular mechanics

Journal: 

Cardiovascular Mechanics, M. F. Labrosse (ed.), CRC Press, p. pp. 54

Date: 

2018

Authors: 

F. Auricchio, M. Conti, A. Lefieux, S. Morganti, A. Reali, G. Rozza, and A. Veneziani

Computational models are bringing novel perspectives into the investigation of cardiovascular issues. Together with imaging improvements, computational tools are increasingly adopted toward the understanding of patient-specific pathological situations, in the development of surgical planning, and in the support of interventional medical decisions. However, the complexity of patient-specific problems calls for an adequate and knowledgeable use of computational tools to obtain valuable results.

A POD-selective inverse distance weighting method for fast parametrized shape morphing

Journal: 

International Journal for Numerical Methods in Engineering

Date: 

2018

Authors: 

F. Ballarin, A. D’Amario, S. Perotto, and G. Rozza

Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid‐structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade‐off reached in terms of accuracy and efficiency.

Combined Parameter and Model Reduction of Cardiovascular Problems by Means of Active Subspaces and POD-Galerkin Methods

Journal: 

Mathematical and Numerical Modeling of the Cardiovascular System and Applications

Date: 

2018

Authors: 

M. Tezzele, F. Ballarin, and G. Rozza

In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid. A parametric description of the admissible deformations, based on radial basis functions interpolation, is introduced. Since the parameter space may be very large, the first step in the combined reduction technique is to look for active subspaces in order to reduce the parameter space dimension.

Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier–Stokes equations

Journal: 

Computers & Fluids

Date: 

2018

Authors: 

G. Stabile and G. Rozza

In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier–Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a finite volumes approximation. The reduced basis spaces are constructed with a POD approach. Two different pressure stabilisation strategies are proposed and compared: the former one is based on the supremizer enrichment of the velocity space, and the latter one is based on a pressure Poisson equation approach.

A Spectral Element Reduced Basis Method in Parametric CFD

Journal: 

Numerical Mathematics and Advanced Applications – ENUMATH 2017, Springer, vol. 126

Date: 

2018

Authors: 

M. W. Hess and G. Rozza

We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization.

Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering

Journal: 

SIAM Journal on Scientific Computing, 40(4), p. pp. B1055-B1079

Date: 

2018

Authors: 

M. Strazzullo, F. Ballarin, R. Mosetti, and G. Rozza

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort.

Computational methods in cardiovascular mechanics

Journal: 

Cardiovascular Mechanics, M. F. Labrosse (ed.), CRC Press, p. pp. 54

Date: 

2018

Authors: 

F. Auricchio, M. Conti, A. Lefieux, S. Morganti, A. Reali, G. Rozza, and A. Veneziani

The introduction of computational models in cardiovascular sciences has been progressively bringing new and unique tools for the investigation of the physiopathology. Together with the dramatic improvement of imaging and measuring devices on one side, and of computational architectures on the other one, mathematical and numerical models have provided a new, clearly noninvasive, approach for understanding not only basic mechanisms but also patient-specific conditions, and for supporting the design and the development of new therapeutic options.

Shape Optimization by means of Proper Orthogonal Decomposition and Dynamic Mode Decomposition

Journal: 

Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research, 2018, p. pp. 212–219

Date: 

2018

Authors: 

N. Demo, M. Tezzele, G. Gustin, G. Lavini, and G. Rozza

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling, applied to a naval hull design problem. The advantage introduced by this method is that the solution for a specific parameter can be expressed as the combination of few numerical solutions computed at properly chosen parametric points. The reduced model is built using the proper orthogonal decomposition with interpolation (PODI) method.

Model order reduction by means of active subspaces and dynamic mode decomposition for parametric hull shape design hydrodynamics

Journal: 

Technology and Science for the Ships of the Future: Proceedings of NAV 2018: 19th International Conference on Ship & Maritime Research, 2018, p. pp. 569–576

Date: 

2018

Authors: 

M. Tezzele, N. Demo, M. Gadalla, A. Mola, and G. Rozza

We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters on the hull wave resistance. Such problem is relevant at the preliminary stages of the ship design, when several flow simulations are carried out by the engineers to establish a certain sensibility with respect to the parameters, which might result in a high number of time consuming hydrodynamic simulations.

Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models

Journal: 

Journal of Scientific Computing, 74, pp. 197-219

Date: 

2018

Authors: 

I. Martini, B. Haasdonk, and G. Rozza

We present a model order reduction approach for parametrized laminar flow problems including viscous boundary layers. The viscous effects are captured by the incompressible Navier–Stokes equations in the vicinity of the boundary layer, whereas a potential flow model is used in the outer region. By this, we provide an accurate model that avoids imposing the Kutta condition for potential flows as well as an expensive numerical solution of a global viscous model. To account for the parametrized nature of the problem, we apply the reduced basis method.

An efficient shape parametrisation by free-form deformation enhanced by active subspace for hull hydrodynamic ship design problems in open source environment

Journal: 

The 28th International Ocean and Polar Engineering Conference

Date: 

2018

Authors: 

N. Demo, M. Tezzele, A. Mola, and G. Rozza

In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess the influence of the shape parameters considered on the hull total drag. The hull resistance is typically computed by means of numerical simulations of the hydrodynamic flow past the ship.

Model Reduction Methods

Journal: 

Encyclopedia of Computational Mechanics Second Edition), John Wiley & Sons, pp. 1-36

Date: 

2017

Authors: 

F. Chinesta, A. Huerta, G. Rozza, and K. Willcox

Reduced-order semi-implicit schemes for fluid-structure interaction problems

Journal: 

Model Reduction of Parametrized Systems, P. Benner, M. Ohlberger, A. Patera, G. Rozza, and K. Urban (eds.), Springer International Publishing, p. pp. 149–167

Date: 

2017

Authors: 

F. Ballarin, G. Rozza, and Y. Maday

POD–Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam operator-splitting approach. Two different reduced-order methods are proposed, which differ on velocity continuity condition, imposed weakly or strongly, respectively. The resulting ROMs are tested and compared on a representative haemodynamics test case characterized by wave propagation, in order to assess the capabilities of the proposed strategies.

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts

Journal: 

Biomechanics and Modeling in Mechanobiology, 16(4), p. pp. 1373–1399

Date: 

2017

Authors: 

F. Ballarin, E. Faggiano, A. Manzoni, A. Quarteroni, G. Rozza, S. Ippolito, C. Antona, and R. Scrofani

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the haemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patientspecific medical images to fast parametrized computational simulations, is proposed.

A reduced order model for investigating the dynamics of the Gen-IV LFR coolant pool

Journal: 

Applied Mathematical Modelling, 46, pp. 263-284

Date: 

2017

Authors: 

S. Lorenzi, A. Cammi, L. Luzzi, and G. Rozza

In the control field, the study of the system dynamics is usually carried out relying on lumped-parameter or one-dimensional modelling. Even if these approaches are well suited for control purposes since they provide fast-running simulations and are easy to linearize, they may not be sufficient to deeply assess the complexity of the systems, in particular where spatial phenomena have a significant impact on dynamics. Reduced Order Methods (ROM) can offer the proper trade-off between computational cost and solution accuracy.

Pod-Galerkin Reduced Order Methods for CFD Using Finite Volume Discretisation: Vortex Shedding Around a Circular Cylinder

Journal: 

Communication in Applied Industrial Mathematics, 8(1), p. pp. 210–236

Date: 

2017

Authors: 

G. Stabile, S. N. Hijazi, S. Lorenzi, A. Mola, and G. Rozza

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach.

On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics

Journal: 

Journal of Scientific Computing

Date: 

2017

Authors: 

G. Pitton and G. Rozza

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers.

Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology

Journal: 

Journal of Computational Physics, 344, p. pp. 557

Date: 

2017

Authors: 

G. Pitton, A. Quaini, and G. Rozza

We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator.

Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation

Journal: 

Spectral and High Order Methods for Partial Differential Equations), Springer, vol. 119

Date: 

2017

Authors: 

D. Devaud and G. Rozza

In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis (IGA) is a growing research theme in scientific computing and computational mechanics, as well as reduced basis methods for parametric PDEs.

Reduced Basis Methods for Uncertainty Quantification

Journal: 

SIAM/ASA Journal on Uncertainty Quantification, 5, p. pp. 813–869

Date: 

2017

Authors: 

P. Chen, A. Quarteroni, and G. Rozza

In this work we review a reduced basis method for the solution of uncertainty quantification problems. Based on the basic setting of an elliptic partial differential equation with random input, we introduce the key ingredients of the reduced basis method, including proper orthogonal decomposition and greedy algorithms for the construction of the reduced basis functions, a priori and a posteriori error estimates for the reduced basis approximations, as well as its computational advantages and weaknesses in comparison with a stochastic collocation method [I. Babuska, F. Nobile, and R.

On a certified Smagorinsky reduced basis turbulence model

Journal: 

SIAM Journal on Numerical Analysis, 55(6), p. pp. 3047–3067

Date: 

2017

Authors: 

T. Chacón Rebollo, E. Delgado Ávila, M. Gómez Mármol, F. Ballarin, and G. Rozza

In this work we present a reduced basis Smagorinsky turbulence model for steady flows. We approximate the non-linear eddy diffusion term using the Empirical Interpolation Method, and the velocity-pressure unknowns by an independent reduced-basis procedure. This model is based upon an a posteriori error estimation for Smagorinsky turbulence model. The theoretical development of the a posteriori error estimation is based on previous works, according to the Brezzi-Rappaz-Raviart stability theory, and adapted for the non-linear eddy diffusion term.

Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes

Journal: 

Advanced Modeling and Simulation in Engineering Sciences, 3(1), p. pp. 21

Date: 

2016

Authors: 

F. Salmoiraghi, F. Ballarin, L. Heltai, and G. Rozza

In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method.

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives

Journal: 

Proceedings of the ECCOMAS Congress 2016, VII European Conference on Computational Methods in Applied Sciences and Engineering

Date: 

2016

Authors: 

F. Salmoiraghi, F. Ballarin, G. Corsi, A. Mola, M. Tezzele, and G. Rozza

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting.

POD-Galerkin Method for Finite Volume Approximation of Navier-Stokes and RANS Equations

Journal: 

Computer Methods in Applied Mechanics and Engineering, 311, pp. 151-179

Date: 

2016

Authors: 

S. Lorenzi, A. Cammi, L. Luzzi, and G. Rozza

Numerical simulation of fluid flows requires important computational efforts but it is essential in engineering applications. Reduced Order Model (ROM) can be employed whenever fast simulations are required, or in general, whenever a trade-off between computational cost and solution accuracy is a preeminent issue as in process optimization and control.

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Journal: 

Computers and Mathematics with Applications, 71(1), p. pp. 408–430

Date: 

2016

Authors: 

L. Iapichino, A. Quarteroni, and G. Rozza

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for.

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization

Journal: 

Journal of Computational Physics, 315, p. pp. 609–628

Date: 

2016

Authors: 

F. Ballarin, E. Faggiano, S. Ippolito, A. Manzoni, A. Quarteroni, G. Rozza, and R. Scrofani

In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algorithms to face at the same time both the geometrical complexity involved in the description of the vascular network and the huge computational cost entailed by time dependent patient-specific flow simulations. Medical imaging procedures allow to reconstruct patient-specific configurations from clinical data.

Reduced basis approaches in time-dependent non-coercive settings for modelling the movement of nuclear reactor control rods

Journal: 

Communications in Computational Physics, 20(1), p. pp. 23–59

Date: 

2016

Authors: 

A. Sartori, A. Cammi, L. Luzzi, and G. Rozza

In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a staircase strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study.

POD–Galerkin monolithic reduced order models for parametrized fluid-structure interaction problems

Journal: 

International Journal for Numerical Methods in Fluids, 82(12), p. pp. 1010–1034

Date: 

2016

Authors: 

F. Ballarin and G. Rozza

In this paper we propose a monolithic approach for reduced order modelling of parametrized fluid-structure interaction problems based on a proper orthogonal decomposition (POD)–Galerkin method. Parameters of the problem are related to constitutive properties of the fluid or structural problem, or to geometrical parameters related to the domain configuration at the initial time.

A multi-physics reduced order model for the analysis of Lead Fast Reactor single channel

Journal: 

Annals of Nuclear Energy, 87, p. pp. 198–208

Date: 

2016

Authors: 

A. Sartori, A. Cammi, L. Luzzi, and G. Rozza

In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken into account, in time-invariant settings.

Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system

Journal: 

Advances in Computational Mathematics, 41(5), p. pp. 1131–1157

Date: 

2015

Authors: 

I. Martini, G. Rozza, and B. Haasdonk

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced.

Reduced Basis Approximation for the Structural-Acoustic Design based on Energy Finite Element Analysis (RB-EFEA)

Journal: 

CEMRACS 2013 – Modelling and simulation of complex systems: stochastic and deterministic approaches), vol. 48, p. pp. 98–115

Date: 

2015

Authors: 

D. Devaud and G. Rozza

In many engineering applications, the investigation of the vibro-acoustic response of structures is of great interest. Hence, great effort has been dedicated to improve methods in this field in the last twenty years. Classical techniques have the main drawback that they become unaffordable when high frequency impact waves are considered. In that sense, the Energy Finite Element Analysis (EFEA) is a good alternative to those methods. Based on an approximate model, EFEA gives time and locally space-averaged energy densities and has been proven to yield accurate results.

Certified Reduced Basis Methods for Parametrized Partial Differential Equations, 1 ed.

Journal: 

Switzerland: Springer, 2015.

Date: 

2015

Authors: 

J. S. Hesthaven, G. Rozza, and B. Stamm

This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Reduced basis approximation of parametrized advection-diffusion PDEs with high Péclet number

Journal: 

Lecture Notes in Computational Science and Engineering, 103, p. pp. 419–426

Date: 

2015

Authors: 

P. Pacciarini and G. Rozza

In this work we show some results about the reduced basis approximation of advection dominated parametrized problems, i.e. advection-diffusion problems with high Péclet number. These problems are of great importance in several engineering applications and it is well known that their numerical approximation can be affected by instability phenomena. In this work we compare two possible stabilization strategies in the framework of the reduced basis method, by showing numerical results obtained for a steady advection-diffusion problem.

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

Journal: 

International Journal for Numerical Methods in Engineering, 102(5), p. pp. 1136–1161

Date: 

2015

Authors: 

F. Ballarin, A. Manzoni, A. Quarteroni, and G. Rozza

In this work, we present a stable proper orthogonal decomposition–Galerkin approximation for parametrized
steady incompressible Navier–Stokes equations with low Reynolds number.

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

Journal: 

Numerische Mathematik, 133(1), p. pp. 67–102

Date: 

2015

Authors: 

P. Chen, A. Quarteroni, and G. Rozza

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 assumptions on the random input data. The finite element method and the stochastic collocation method are employed for the numerical approximation of the problem in the deterministic space and the probability space, respectively, resulting in many large-scale optimality systems to solve.

Fundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications

Journal: 

Separated representations and PGD-based model reduction: fundamentals and applications), Springer, vol. 554

Date: 

2014

Authors: 

G. Rozza

In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method.

Reduced Order Methods for Modeling and Computational Reduction, 1 ed.

Journal: 

Springer, 2014, vol. 9.

Date: 

2014

Authors: 

A. Quarteroni and G. Rozza

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

A weighted empirical interpolation method: A priori convergence analysis and applications

Journal: 

ESAIM: Mathematical Modelling and Numerical Analysis, 48(4), p. pp. 943–953

Date: 

2014

Authors: 

P. Chen, A. Quarteroni, and G. Rozza

We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667-672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions.

Stabilized reduced basis method for parametrized advection-diffusion PDEs

Journal: 

Computer Methods in Applied Mechanics and Engineering, 274, p. pp. 1–18

Date: 

2014

Authors: 

P. Pacciarini and G. Rozza

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Journal: 

Journal of Scientific Computing, 59(1), p. pp. 187–216

Date: 

2014

Authors: 

P. Chen, A. Quarteroni, and G. Rozza

The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45(3):1005-1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411-2442, 2008a; SIAM J Numer Anal 46(5):2309-2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118-1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al.

An improvement on geometrical parameterizations by transfinite maps

Journal: 

Comptes Rendus Mathematique, 352(3), p. pp. 263–268

Date: 

2014

Authors: 

C. Jäggli, L. Iapichino, and G. Rozza

We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries.

Model order reduction in fluid dynamics: challenges and perspectives

Journal: 

Reduced Order Methods for Modeling and Computational Reduction, A. Quarteroni and G. Rozza (eds.), Springer MS&A Series, vol. 9, p. pp. 235–274

Date: 

2014

Authors: 

T. Lassila, A. Manzoni, A. Quarteroni, and G. Rozza

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities - which are mainly related either to nonlinear convection terms and/or some geometric variability - that often cannot be treated by simple linearization.

Stabilized reduced basis method for parametrized scalar advection-diffusion problems at higher Péclet number: Roles of the boundary layers and inner fronts

Journal: 

11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, p. pp. 5614–5624.

Date: 

2014

Authors: 

P. Pacciarini and G. Rozza

Advection-dominated problems, which arise in many engineering situations, often require a fast and reliable approximation of the solution given some parameters as inputs. In this work we want to investigate the coupling of the reduced basis method - which guarantees rapidity and reliability - with some classical stabilization techiques to deal with the advection-dominated condition. We provide a numerical extension of the results presented in [1], focusing in particular on problems with curved boundary layers and inner fronts whose direction depends on the parameter.

Shape Optimization by Free-Form Deformation: Existence Results and Numerical Solution for Stokes Flows

Journal: 

Journal of Scientific Computing, 60(3), p. pp. 537–563

Date: 

2014

Authors: 

F. Ballarin, A. Manzoni, G. Rozza, and S. Salsa

Shape optimization problems governed by PDEs result from many applications in computational fluid dynamics. These problems usually entail very large computational costs and require also a suitable approach for representing and deforming efficiently the shape of the underlying geometry, as well as for computing the shape gradient of the cost functional to be minimized. Several approaches based on the displacement of a set of control points have been developed in the last decades, such as the so-called free-form deformations.

A reduced order model for multi-group time-dependent parametrized reactor spatial kinetics

Journal: 

International Conference on Nuclear Engineering, Proceedings, ICONE

Date: 

2014

Authors: 

A. Sartori, D. Baroli, A. Cammi, L. Luzzi, and G. Rozza

In this work, a Reduced Order Model (ROM) for multigroup time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity ``truth'' finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter.

Comparison of a Modal Method and a Proper Orthogonal Decomposition approach for multi-group time-dependent reactor spatial kinetics

Journal: 

Annals of Nuclear Energy, 71, p. pp. 217–229

Date: 

2014

Authors: 

A. Sartori, D. Baroli, A. Cammi, D. Chiesa, L. Luzzi, R. Ponciroli, E. Previtali, M. E. Ricotti, G. Rozza, and M. Sisti

In this paper, two modelling approaches based on a Modal Method (MM) and on the Proper Orthogonal Decomposition (POD) technique, for developing a control-oriented model of nuclear reactor spatial kinetics, are presented and compared. Both these methods allow developing neutronics description by means of a set of ordinary differential equations. The comparison of the outcomes provided by the two approaches focuses on the capability of evaluating the reactivity and the neutron flux shape in different reactor configurations, with reference to a TRIGA Mark II reactor.

Reduced basis method for the Stokes equations in decomposable domains using greedy optimization

Journal: 

ECMI 2014 proceedings, p. pp. 1–7

Date: 

2014

Authors: 

L. Iapichino, A. Quarteroni, G. Rozza, and S. Volkwein

In this paper we present a reduced order method for the solution of parametrized Stokes equations in domain composed by an arbitrary number of predefined shapes. The novelty of the proposed approach is the possibility to use a small set of precomputed bases to solve Stokes equations in very different computational domains, defined by combining one or more reference geometries. The selection of the basis functions is performed through an optimization greedy algorithm.

A reduced computational and geometrical framework for inverse problems in hemodynamics

Journal: 

International Journal for Numerical Methods in Biomedical Engineering, 29(7), p. pp. 741–776

Date: 

2013

Authors: 

T. Lassila, A. Manzoni, A. Quarteroni, and G. Rozza

The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier-Stokes equations by a computationally less-expensive reduced-basis approximation. This greatly reduces the cost of simulating the forward problem.

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

Journal: 

ESAIM: Mathematical Modelling and Numerical Analysis, 47(4), p. pp. 1107–1131

Date: 

2013

Authors: 

T. Lassila, A. Manzoni, A. Quarteroni, and G. Rozza

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.

Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: Roles of the inf-sup stability constants

Journal: 

Numerische Mathematik, 125(1), p. pp. 115–152

Date: 

2013

Authors: 

G. Rozza, D. B. P. Huynh, and A. Manzoni

In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi's and Babuška's stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an affine parametric dependence enabling to perform competitive Offline-Online splitting in the computational procedure and a rigorous a posteriori error estimation on field variables.

Reduced basis method for parametrized elliptic optimal control problems

Journal: 

SIAM Journal on Scientific Computing, 35(5), p. pp. A2316–A2340

Date: 

2013

Authors: 

F. Negri, G. Rozza, A. Manzoni, and A. Quarteroni

Free Form Deformation Techniques Applied to 3D Shape Optimization Problems

Journal: 

Communications in Applied and Industrial Mathematics

Date: 

2013

Authors: 

A. Koshakji, A. Quarteroni, and G. Rozza

Generalized reduced basis methods and n-width estimates for the approximation of the solution manifold of parametric PDEs

Journal: 

Analysis and Numerics of Partial Differential Equations, F. Brezzi, P. Colli Franzone, U. Gianazza, and G. Gilardi (eds.), , vol. 4, p. pp. 307–329

Date: 

2013

Authors: 

T. Lassila, A. Manzoni, A. Quarteroni, and G. Rozza

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.

Reduction strategies for shape dependent inverse problems in haemodynamics

Journal: 

IFIP Advances in Information and Communication Technology, 391 AICT, p. pp. 397–406

Date: 

2013

Authors: 

T. Lassila, A. Manzoni, and G. Rozza

This work deals with the development and application of reduction strategies for real-time and many query problems arising in fluid dynamics, such as shape optimization, shape registration (reconstruction), and shape parametrization. The proposed strategy is based on the coupling between reduced basis methods for the reduction of computational complexity and suitable shape parametrizations - such as free-form deformations or radial basis functions - for low-dimensional geometrical description.

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

Journal: 

Comptes Rendus Mathematique, 351(15-16), p. pp. 593–598

Date: 

2013

Authors: 

D. Devaud, A. Manzoni, and G. Rozza

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 of a three-step RB-ANOVA-RB method. This is a combination of the reduced basis (RB) method and the analysis of variations (ANOVA) expansion, aiming at compressing the parameter space without affecting the accuracy of the output.

Simulation-based uncertainty quantification of human arterial network hemodynamics

Journal: 

International Journal for Numerical Methods in Biomedical Engineering, 29(6), p. pp. 698–721

Date: 

2013

Authors: 

P. Chen, A. Quarteroni, and G. Rozza

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 characterization with log-normal distribution of these uncertainties is introduced.

Reduction strategies for PDE-constrained optimization problems in haemodynamics

Journal: 

ECCOMAS 2012 – European Congress on Computational Methods in Applied Sciences and Engineering, p. pp. 1749–1768

Date: 

2012

Authors: 

G. Rozza, A. Manzoni, and F. Negri

Solving optimal control problems for many different scenarios obtained by varying a set of parameters in the state system is a computationally extensive task. In this paper we present a new reduced framework for the formulation, the analysis and the numerical solution of parametrized PDE-constrained optimization problems.