Sixth deal.II Users and Developers Workshop

Jul 23 – 27, 2018
SISSA Main Building
Europe/Rome timezone

Algorithms and data structures for matrix-free finite element operators with MPI-parallel sparse multi-vectors

Jul 26, 2018, 9:00 AM
45m
Meeting Room -- VII Floor (SISSA Main Building)

Meeting Room -- VII Floor

SISSA Main Building

Via Bonomea 265 34136 -- Trieste -- Italy
Keynote presentations Developers' track

Speaker

Denis Davydov (Friedrich-Alexander University Erlangen-Nuremberg)

Description

Traditional solution approaches for problems in quantum mechanics scale as $\mathcal O(N^3)$, where $N$ is the number of electrons. Various methods have been proposed to address this issue and obtain linear scaling $\mathcal O(N)$. One promising formulation is the direct minimization of energy. Such methods take advantage of physical localization of the solution, namely that the solution can be sought in terms of non-orthogonal orbitals with local support. This is often called the near-sightedness principle of matter. In this talk we present numerically efficient implementation of sparse parallel vectors within the deal.II open-source finite element library suitable for matrix-free operator evaluation. Based on the a-priori chosen support for each vector, we develop algorithms and data structures to perform (i) matrix-free sparse matrix multi-vector products (SpMM) (ii) projection of an operator onto a sparse sub-space (inner products) (iii) post-multiplication with a matrix. Strong and weak scaling results are reported for a typical benchmark problem using quadratic and quartic finite element bases.

Primary author

Denis Davydov (Friedrich-Alexander University Erlangen-Nuremberg)

Co-authors

Dr Martin Kronbichler (Technical University of Munich) Prof. Paul Steinmann (Friedrich-Alexander University Erlangen-Nuremberg)

Presentation materials

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