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Numerical Analysis Seminar


Tid: 2022-01-19 15:15 till 16:00
Plats: only via Zoom - please contact organizer for link
Kontakt: alexandros [dot] sopasakis [at] math [dot] lth [dot] se
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PSCToolkit: pushing linear algebra towards the exascale Fabio Durastante, Mathematics, University of Pisa

Sparse linear algebra is essential for a wide variety of scientific applications. The availability of massively parallel sparse solvers and preconditioners lies at the core of pretty much all multi-physics and multi-scale simulations. Technology is nowadays expanding to target exascale platforms, i.e., computing systems capable of calculating at least 1018 floating-point operations per second.

We try to face these challenges by developing both algorithmic and theoretical strategies to make exascale computing possible, these efforts are collected in the set of libraries called Parallel Sparse Computation Toolkit [1] (PSCToolkit: which contain, on one hand, the basic routines for working with distributed linear algebra (MPI) and with GPU accelerators (CUDA), together with experimental support for OpenMP API to support multi-platform shared-memory parallel programming. On the other hand, iterative solvers of Krylov-type and a package of algebraic preconditioners such as several types of domain decomposition and algebraic multigrid preconditioners. In this talk, I will discuss the general idea behind the framework and show its application to both classical benchmark problem (3D Poisson) and more realistic settings (Large Eddy Simulation for wind over terrain and simulation of the water flow in the vadose zone by the
solution of the nonlinear Richards equation [2]).

This is joint work with Pasqua D’Ambra (Institute of Applied Computing "M. Picone" from the Italian National Research Council) and Salvatore Filippone (University of Rome “Tor Vergata”) and was supported by the Horizon 2020 Project Energy oriented Centre of Excellence: Toward Exascale for Energy (EoCoE-II), project ID 824158.

[1] P. D’Ambra, F. D. and S. Filippone, AMG preconditioners for linear solvers towards extreme scale, SIAM J. Sci. Comput. 43 (2021), no. 5, S679–S703.
[2] D. Bertaccini, P. D’Ambra, F. D. and S. Filippone, Preconditioning Richards Equations: spectral analysis and parallel solution at very large scale, submitted (2021), arXiv/2112.05051.