Contour Integral Methods for parametric PDEs and model order reduction (Nicola Guglielmi, L'Aquilla)

25.10.2022 14:00

We present a new class of contour integral methods for linear convection–diffusion PDEs and in particular for those arising in finance.
These methods aim to provide a numerical approximation of the solution by computing its inverse Laplace transform. The choice of the integration contour is determined by a pseudospectral roaming technique, which means it depends on few (weighted) pseudo-spectral level sets of the leading operator of the equation.

Next we present a projection model order reduction method for parametric problems. The main advantage of this approach consists in the fact that, differently from time stepping methods as Runge-Kutta integrators, the Laplace transform allows to compute the solution directly at a given instant. In terms of the reduced basis methodology, this determines a significant improvement in the reduction phase, like the one based on the classical proper orthogonal decomposition (POD), since the number of vectors to which the decomposition applies is significantly reduced as it does not contain intermediate solutions generated along an integration grid by a time stepping method.

Finally we show the behavior of the method on some illustrative examples arising from finance.

This talk is based on joint works with Maria Lopez Fernandez and Mattia Manucci.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire d'analyse numérique

entrée libre