Real-time reduced basis techniques in arterial bypass geometries

3rd M.I.T. Conference on Computational Fluid and Solid Mechanics

Volumn , Issue , 2005, Pages 1284-1287

  Rozza, Gianluigi ^a  

^a EPFL   (Switzerland)

Author keywords

Arterial bypass optimization; Design of improved biomechanical devices; Generalized Stokes problem; Haemodynamics; Parametrized PDEs; Reduced basis methods

Indexed keywords

ARTERIAL BYPASS; ARTERIAL SURGERY; BLOOD FLOW; COMPLETE SOLUTIONS; COMPUTATIONAL COSTS; DYNAMICS EQUATION; FUNCTIONAL OUTPUTS; GENERALIZED STOKES PROBLEM; GEOMETRICAL QUANTITIES; HAEMODYNAMICS; INPUT-OUTPUT; LOWER COMPLEXITY; OPTIMIZATION AND DESIGN; PARAMETRIZED PDES; REDUCED BASIS METHODS; REDUCED BASIS TECHNIQUE;

BIOMECHANICS; COMPUTATIONAL FLUID DYNAMICS; DESIGN; FLUID MECHANICS; FLUIDS; HEMODYNAMICS; NUMERICAL METHODS; OPTIMIZATION; SENSITIVITY ANALYSIS;

FINITE ELEMENT METHOD;

EID: 58149500654     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (9)

1. Quarteroni A, Formaggia L. Mathematical modelling and numerical simulation of the cardiovascular system. In: PG Ciarlet, JL Lions, editors, Modelling of Living Systems, Handbook of Numerical Analysis Series. Amsterdam: Elsevier, 2003.
2. Abraham F, Behr M, Heinkenschloss M. Shape optimization in stationary blood flow: a numerical study of non- Newtonian effects. Submitted to Comput Meth Biomech Biomed Eng, 2004.
3. Quarteroni A, Rozza G. Optimal control and shape optimization of aortocoronaric bypass anastomoses. Math Models Meth Appl Sci, 2003;13(12):1801-1823.
4. Prud'homme C, Rovas D, Veroy K, Maday Y, Patera AT, Turinici G. Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J Fluids Eng 2002;172:70-80.
5. Rozza G. On optimization, control and shape design of an arterial bypass. Int J Numerical Meth Fluids 2005 (in press).
6. Quarteroni A, Valli A. Numerical Approximation of Partial Differential Equations. Berlin: Springer-Verlag, 1994.
7. Patera AT, Rozza G, Veroy K. Reduced basis methodologies for Stokes equations in parametrized domains. EPEL-IACS report 22.2004, 2005.
8. Veroy K, Patera AT. Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Int J Numerical Meth Fluids, 2005 (in press).
9. Barrault M, Maday Y, Nguyen NC, Patera AT. An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations. CR Acad Sci Paris, Analyse Numérique, Serie I, 2004;339:667-672.