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T. M. Lassila, A. Quarteroni, and G. Rozza.
A reduced basis model with parametric coupling for fluid-structure
interaction problems.
Siam Journal on Computing, 2012.
MATHICSE report 01.2011.
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F. Negri, A. Quarteroni, and G. Rozza.
Reduced basis method for parametrized optimal control problems
governed by PDEs.
Master thesis developed at EPFL in the framework of an Erasmus
exchange with Politecnico di Milano, 2011.
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A. Manzoni, A. Quarteroni, and G. Rozza.
Shape optimization for viscous flows by reduced basis methods and
free-form deformation.
International Journal for Numerical Methods in Fluids,
2011.
MATHICSE report 15.2010.
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R. Bank, W. Hackbusch, G. Wittum, A. Quarteroni, A. Manzoni, and G. Rozza.
Model order reduction by reduced basis methods and free-form
deformations for shape optimization.
In Schnelle Löser für Partielle
Differentialgleichungen, number 28 in Mathematisches Forschungsinstitut
Oberwolfach, pages 19-22, Oberwolfach, Germany, 2011.
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A. Manzoni, A. Quarteroni, and G. Rozza.
Model reduction techniques for fast blood flow simulation in
parametrized geometries.
International Journal for Numerical Methods in
Biomedical Engineering, 2011.
MATHICSE report 05.2011.
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Modelling of Physiological Flows, MS&A, Modelling, Simulation and
Applications, Milano, 2011. Springer.
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A. Quarteroni, G. Rozza, and A. Manzoni.
Certified Reduced Basis Approximation for Parametrized
Partial Differential Equations and Applications.
Journal of Mathematics in Industry, 1:3:1-44, 2011.
MATHICSE report 02.2011.
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A. Koshakji, A. Quarteroni, and G. Rozza.
Free Form Deformation Techniques for 3D Shape
Optimization Problems.
This master thesis has been developed in the framework of the
EU-Socrates program as exchange student from Politecnico di Milano at EPFL
Lausanne, 2011.
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F. Gelsomino and G. Rozza.
Comparison and combination of reduced order modelling techniques in
3D parametrized heat transfer problems.
Mathematical and Computer Modelling of Dynamical
Systems, 17(4):371-394, 2011.
Special issue on model order reduction, previously EPFL MATHICSE
report 12.2010.
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T. M. Lassila and G. Rozza.
Model reduction of semiaffinely parameterized partial differential
equations by two-level affine approximation.
Comptes rendus des séances de l'Académie des Sciences.
Série A, Sciences mathématiques**, 349:61-66, 2011.
MATHICSE report 20.2010.
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G. Rozza.
Reduced basis approximation and error bounds for potential flows in
parametrized geometries.
Communications in Computational Physics, 9(1):1-48, 2011.
preprint as MATHICSE report 11.2010.
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R. A. E. Makinen, K. Valpe, P. Neittaanmaki, T. Tuovinen, T. M. Lassila, and
G. Rozza.
Reduced formulation of a steady fluid-structure interaction problem
with parametric coupling.
In Proceedings of the 10th Finnish Mechanics Days
Conference, 2010.
MATHICSE report 13.2010.
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A. Trezzini, A. Quarteroni, and G. Rozza.
Reduced Basis Method for 3D Problems governed by
Parametrized PDEs and Applications.
This thesis was developed at EPFL in the framework of the EU-Socrates
project as exchange student from Politecnico di Milano, 2010.
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J. C. F. Pereira, A. Sequeira, G. Rozza, and A. Manzoni.
Model Order Reduction by geometrical parametrization for shape
optimization in computational fluid dynamics.
In Proceedings of the ECCOMAS CFD 2010, V European
Conference on Computational Fluid Dynamics, Lisbon, Portugal, 2010.
MATHICSE Report 05.2010.
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F. Gelsomino, A. Quarteroni, and G. Rozza.
Exploration and comparison of reduced order modelling techniques for
parametrized systems.
Master Thesis EPFL, winter semester 2009-2010, 2010.
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E. Ronquist, J. Hesthaven, G. Rozza, T. M. Lassila, and A. Manzoni.
Reduced basis approximation for shape optimization in thermal flows
with a parametrized polynomial geometric map.
In Spectral and High Order Methods for Partial
Differential Equations, volume 76 of Lecture Notes in Computational
Science and Engineering, pages 307-315, Heildeberg, 2010. Springer.
EPFL MATHICSE report 02.2010.
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T. M. Lassila and G. Rozza.
Parametric free-form shape design with PDE models and reduced basis
method.
Computer Methods in Applied Mechanics and Engineering,
199(23-24):1583-1592, 2010.
EPFL MATHICSE report 01.2010.
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Z. Xuan, T. M. Lassila, G. Rozza, and A. Quarteroni.
Computing upper and lower bounds for linear outputs of elasticity by
the smoothed finite element method.
Int. J. Numer. Meth. Engng., 83(2):174-195, 2010.
previously IACS report 07.2009.
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L. Tenorio, B. van Bloemen Waanders, B. Mallick, K. Willcox, L. Biegler,
G. Biros, O. Ghattas, M. Heinkenschloss, D. Keyes, Y. Marzouk, C. Nguyen,
G. Rozza, D. B. P. Huynh, and A. T. Patera.
Reduced basis approximation and a posteriori error estimation for
parametrized parabolic PDEs; Application to real-time Bayesian
parameter estimation.
In Large Scale Inverse Problems and Quantification of
Uncertainty, number Chapter 8 in Wiley Series in Computational Statistics,
pages 151-178. John Wiley & Sons, UK, 2010.
EPFL-IACS report 11.2008.
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G. Rozza, E. De Bernardis, R. Spiegler, and V. Valente.
An introduction to reduced basis method for parametrized PDEs.
In Applied and Industrial Mathematics in Italy, volume
III of Advances in Mathematics for Applied Sciences, pages 508-519,
Singapore, 2009. WorldScientific.
EPFL-IACS report 01.09, peer reviewed.
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G. Rozza, N. C. Nguyen, A. T. Patera, and S. Deparis.
Reduced Basis Methods and A Posteriori Error Estimators
for Heat Transfer Problems.
In Proceedings of the ASME HT 2009 summer conference, Heat
Transfer Confererence, New York, 2009. ASME.
presented in the Computational Section of the conference. EPFL-IACS
report 05.2009, peer reviewed.
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G. Rozza, D. P. Huynh, N. C. Nguyen, and A. T. Patera.
Real-Time Reliable Simulation of Heat Transfer Phenomena.
In Proceedings of the ASME HT 2009 summer conference, Heat
Transfer Confererence, NewYork, 2009. ASME.
presented in the Educational Section of the conference. EPFL-IACS
report 06.2009, peer reviewed.
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E. Zuazua, C. Le Bris, A. Patera, A. Quarteroni, T. Hou, G. Rozza, and
A. Quarteroni.
Reduced basis approximation for parametrized partial differential
equations.
In Numerical Models for Differential Equations, volume
Chapter 18 of MS&A, Modelling, Simulation and Application, pages
556-587. Springer, Heildelberg, 2009.
EPFL-IACS report 04.2009.
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S. Deparis and G. Rozza.
Reduced basis method for multi-parameter dependent steady
Navier-Stokes equations: applications to natural convection in a cavity.
Journal of Computational Physics, 228(12):4359-4378, 2009.
EPFL-IACS report 12.2008.
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N. C. Nguyen, G. Rozza, and A. T. Patera.
Reduced Basis Approximation and A Posteriori Error
Estimation for the Time- Dependent Viscous Burgers Equation.
Calcolo, 46(3):157-185, 2009.
previously EPFL-IACS Report 10.2008.
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G. Rozza.
Reduced basis methods for Stokes equations in domains with
non-affine parameter dependence.
Computing and Visualization in Science, 12(1):23-35, 2009.
published online since November 2006.
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G. Grandperrin, G. Rozza, and A. Quarteroni.
Introduction a la methode des bases reduites.
Reduced Basis method elliptic coercive partial differential
equations, 2008.
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C. Gunther, G. Rozza, S. Deparis, A. Quarteroni, and M. Behr.
Reduced basis method for the shape optimization of racing car
components.
Claudia Gunther has been at EPFL as visiting master degree student
from University of Aachen (Germany), 2008.
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R. Milani, A. Quarteroni, and G. Rozza.
Reduced basis method for linear elasticity problems with many
parameters.
Computational Methods in Applied Mechanics and
Engineering, 197(51-52):4812-4829, 2008.
EPFL-IACS report 03.2008.
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B. Haasdonk, M. Ohlberger, and G. Rozza.
A Reduced Basis Method for Evolution Schemes with
Parameter-Dependent Explicit Operators.
ETNA, Electronic Transactions on Numerical Analysis,
32:145-168, 2008.
Previously EPFL-IACS report 09.2008. Selected Paper from the 20th
Chemnitz Finite Element Symposium, special issue on new developments in the
field of numerical methods for partial differential equations and their
applications.
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G. Rozza, D. B. P. Huynh, and A. T. Patera.
Reduced basis approximation and a posteriori error estimation for
affinely parametrized elliptic coercive partial differential equations:
Application to transport and continuum mechanics.
Archives of Computational Methods in Engineering,
15(3):229-275, 2008.
Invited review paper on the occasion of the ECCOMAS PhD Award
received by the first author in 2006.
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A. T. Patera and G. Rozza.
Reduced Basis Approximation and A Posteriori Error
Estimation for Parametrized Partial Differential Equations.
MIT-Pappalardo Graduate Monographs in Mechanical Engineering. (C)
MIT, Massachusetts Institute of Technology, Cambridge, MA, US, 2007.
Please cite as: A.T. Patera and G. Rozza, Reduced Basis Approximation
and A Posteriori Error Estimation for Parametrized Partial Differential
Equations, Version 1.0, Copyright MIT 2006–2007, to appear in (tentative
rubric) MIT Pappalardo Graduate Monographs in Mechanical Engineering.
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D. B. P. Huynh, G. Rozza, S. Sen, and A. T. Patera.
A successive constraint linear optimization method for lower bounds
of parametric coercivity and inf-sup stability constants.
C. R. Math. Acad. Sci. Paris, 345(8):473-478, 2007.
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A. Quarteroni and G. Rozza.
Tecniche a Basi Ridotte per l'Ottimizzazione di
Configurazioni di Innesto per Bypass Coronarici.
In Un grande matematico dell'800: omaggio a Eugenio
Beltrami, Quaderni Incontro di Studio, Istituto Lombardo, Accademia di
Scienze e Lettere, Milano, Italy, pages 225-238, 2007.
[ Details ]
G. Rozza and K. Veroy.
On the stability of Reduced Basis methods for Stokes
Equations in parametrized domains.
Computer Methods in Applied Mechanics and Engineering,
196(7):1244-1260, 2007.
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A. Quarteroni and G. Rozza.
Numerical solution of parametrized Navier-Stokes equations by
reduced basis methods.
Numerical Methods for Partial Differential Equations,
23(4):923-948, 2007.
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A. Quarteroni, G. Rozza, A. Quaini, W. Fitzgibbon, R. Hoppe, J. Periaux,
O. Pironneau, and Y. Vassilevski.
Reduced basis methods for optimal control of advection-diffusion
problems.
In Advances in Numerical Mathematics, pages 193-216,
Moscow, Russia and Houston, USA, 2007.
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R. Milani, G. Rozza, and A. Quarteroni.
Metodi a basi ridotte per la risoluzione di problemi parametrizzati
in elasticita' lineare.
Master thesis developed at EPFL in the framework of EU Socrates
Project when the author was student at Politecnico di Milano and at EPFL as
visiting/ international exchange student., 2006.
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G. Fourestey, N. Parolini, C. Prud'homme, A. Quarteroni, and G. Rozza.
Matematica in volo con Solar Impulse.
In Matematica e Cultura 2006, pages 35-48, 2006.
[ Details ]
G. Rozza.
Real-time reduced basis solutions for Navier-Stokes equations:
optimization of parametrized bypass configurations.
In ECCOMAS CFD 2006 Proceedings on CD, 2006.
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A. Quarteroni, G. Rozza, L. Dedè, and A. Quaini.
Numerical approximation of a control problem for advection-diffusion
processes.
In System modeling and optimization, volume 199, pages
261-273. Springer, Boston, 2006.
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V. Agoshkov, A. Quarteroni, and G. Rozza.
Shape design in aorto-coronaric bypass anastomoses using perturbation
theory.
SIAM Journal on Numerical Analysis, 44(1):367-384,
2006.
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V. Agoshkov, A. Quarteroni, and G. Rozza.
A mathematical approach in the design of arterial bypass using
unsteady Stokes equations.
Journal of Scientific Computing, 28(2-3):139-165, 2006.
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A. Quaini, G. Rozza, and A. Quarteroni.
Metodi a basi ridotte per problemi differenziali di fluidodinamica
ambientale.
Master thesis developed at EPFL in the framework of EU Socrates
Project when the author was student at Politecnico di Milano and at EPFL as
visiting/ international exchange student., 2005.
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G. Rozza.
Reduced-basis methods for elliptic equations in sub-domains with a
posteriori error bounds and adaptivity.
Applied Numerical Mathematics, 55(4):403-24, 2005.
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G. Rozza.
On optimization, control and shape design of an arterial bypass.
International Journal for Numerical Methods in Fluids,
47(10-11):1411-19, 2005.
[ DOI |
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G. Rozza.
Real time reduced basis techniques for arterial bypass geometries.
In Computational Fluid and Solid Mechanics - Third
M.I.T. Conference on Computational Fluid and Solid Mechanics,
pages 1283-1287, 2005.
[ Details ]
G. Rozza and A. Quarteroni.
Shape design by optimal flow control and reduced basis
techniques.
PhD thesis, Lausanne, 2005.
ECCOMAS (European Community on Computational Methods in Applied
Sciences) Award for the Best Ph.D Thesis on Computational Methods in Applied
Sciences and Engineering (2005).
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L. Dede, G. Rozza, and A. Quarteroni.
Controllo ottimale e adattivita' per equazioni alle derivate parziali
e applicazioni.
Master thesis developed at EPFL in the framework of EU Socrated
Project when the author was student at Politecnico di Milano and at EPFL as
visiting/ international exchange student., 2004.
[ Details |
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A. Quarteroni and G. Rozza.
Optimal control and shape optimization of aorto-coronaric bypass
anastomoses.
Mathematical Models and Methods in Applied Sciences,
13(12):1801-1823, 2003.
[ DOI |
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G. Rozza and A. Quarteroni.
Controllo ottimale e ottimizzazione di forma in fluidodinamica
numerica.
Master thesis developed at EPFL in the framework of EU Socrated
Project when the author was student at Politecnico di Milano and at EPFL as
visiting/ international exchange student., 2002.
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