Speaker: Simone Brugiapaglia
Affiliation: Politecnico di Milano --- Laboratory for Modeling and
Scientific Computing MOX
Time: Tuesday, December 15, 11 am
Place: Sala Seminari Est, Dipartimento di Informatica, Università di Pisa
Title: CORSING: Sparse approximation of PDEs based on Compressed Sensing
Abstract: We present a novel method for the numerical approximation of
PDEs, motivated by recent developments in sparse representation, and
particularly by compressed sensing. We named this approach CORSING
(COmpRessed SolvING).
Establishing an analogy between the sampling of a signal and the
Petrov-Galerkin discretization of a PDE, the CORSING method can recover
the best s-term approximation to the solution with respect to N suitable
trial functions, with s<<N, by evaluating the bilinear form associated
with the PDE against a randomized choice of m<<N test functions. This
yields an underdetermined m x N linear system, that is solved by means
of sparse optimization techniques.
A theoretical analysis of the CORSING procedure is presented, based on
the concepts of local a-coherence and restricted inf-sup property, along
with numerical experiments that confirm the robustness and reliability
of the proposed strategy.
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Everyone is welcome!
--
--federico poloni
