4 Aprile, 2016 10:30

Dipartimento di Matematica del Politecnico di Milano

CANCELLATO causa motivi familiari --- Generalized parametric solutions for optimal design and patient-specific simulations

P. Diez, Universitat Politecnica de Catalunya BarcelonaTech, Spain

Aula Consiglio VII Piano Dipartimento di Matematica, Politecnico di Milano

SEMINARIO TENUTO NELL'AMBITO DEL CORSO DI DOTTORATO: "METODI NUMERICI AVANZATI NEL CALCOLO SCIENTIFICO"

Reduced order models are nowadays a standard approach to represent a solution with less degrees of freedom than in the original model. The large majority of available approaches requires first an offline calculation and, second, solving a problem in an online phase. A particular and singular feature of the Proper Generalized Decomposition (PGD) is that the offline computation provides a generalized parametric solution, also referred as computational vademecum, precluding the need of solving any problem in the second phase. This results from taking the parameters as if they were standard physical coordinates (space and/or time). Thus, user-prescribed parameters like material constants, external loads, geometry, etc. have a similar treatment as the usual coordinates. Consequently, the online phase consists merely in a functional evaluation and therefore is very efficient from a computational viewpoint. Moreover, the generalized parametric solution can be further exploited by making use of the explicit form of the parametric dependence (viz. Fourier transform, gradients for sensibilities, …). The separation in spatial dimensions (and time in some cases), material and geometrical parameters allows for a drastic reduction in computational costs.
This approach is extremely efficient in different applications. We discuss two cases in which the geometrical parameterization of the problem is accounted for in the computational vademecum: 1) optimal automotive shape design parameterizing the aerodynamic external flow, and 2) medical diagnosis and support for decision-making via real-time simulations based on patient-specific data.

contact: simona.perotto@polimi.it