Approximated Lax Pair for reduced order modeling. Application to electrophysiology

J.F. Gerbeau

Inria Paris

Monday 30th March 2015

14:30:00

Aula Saleri VI Piano MOX Dipartimento di Matematica POLITECNICO DI MILANO

A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line / on-line strategy. Numerical examples are shown for the FKPP equations and for the bidomain model of electrophysiology. This work was done in collaboration with Damiano Lombardi and Elisa Schenone. contact: christian.vergara@polimi.it