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Francesco Tudisco

Associate Professor

School of Mathematics

GSSI Gran Sasso Science Institute

Web: https://ftudisco.gitlab.io

 

 

Stefano Massei
University of Pisa, Italy
https://sites.google.com/view/stefanomassei/home


Title of the talk:
Improved parallel-in-time integration via low-rank updates and interpolation

Abstract:
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of parallel-in-time integration leading to a class of algorithms called ParaDiag. We develop and analyze two novel approaches for the numerical solution of such equations. Our first approach is based on the observation that the modification of these equations performed by ParaDiag in order to solve them in parallel has low rank. Building upon previous work on low-rank updates of matrix equations, this allows us to make use of tensorized Krylov subspace methods to account for the modification. Our second approach is based on interpolating the solution of the matrix equation from the solutions of several modifications. Both approaches avoid the use of iterative refinement needed by ParaDiag and related space-time approaches in order to attain good accuracy. In turn, our new approaches have the potential to outperform, sometimes significantly, existing approaches. This potential is demonstrated for several different types of PDEs.


For more information, please see:
https://num-gssi.github.io/seminar/

The seminar will take place in the Main Lecture Hall, but remote participation will also be possible via the zoom link:
https://us02web.zoom.us/j/89668910844?pwd=TmVwQUFoNklUajAzMlEyMzB6ZVZzUT09