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Proposing Institution

RWTH Aachen University
Project Manager

Jan Winkelmann
Schinkelstraße 2
52062 Aachen
Many material science simulations, including Plane Wave methods, require the solution to large Hermitian eigenvalue problems.The simulation of larger and larger physical systems requires increasing amounts of parallelism.As a result eigensolvers based on Subspace Iteration (SI) have regained the attention of the research community in recent years.Modern implementations use filtering in order to improve the convergence of the SI procedure.These filters are polynomial or rational matrix-valued function, resulting in respectively large matrix-matrix multiplications or linear system solves.The current challenges for these kinds of solvers are twofold:First, implementing and leveraging parallelism.Matrix-matrix multiplications, if properly implemented, can achieve a significant percentage of peak.With the increasing heterogeneity of recent supercomputers, including GPUs and Many-Core processors, more and more effort is required to realize good performance for parallel GEMM.This project would equip us with additional hardware to test and tune our own parallel matrix-matrix multiplication routines.Second, parameter selection.While there exist a mathematical proof for an optimal filter, this is not the case for rational filters.It is possible to improve state-of-the-art rational filters via optimization methods.Not only is the optimization procedure expensive, but the resulting filters require test runs for validation purposes.This project would allow us to further improve rational filters for Subspace Iteration, thus improving performance for Material Science codes.

Impressum, Conny Wendler