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Paul F. Fischer
Mathematics and Computer Science Division
Argonne National Laboratory, USA

September 3, 2012, 17:10 Apéro, 17:30 Seminar
Auditorium F2, KTH Main Campus, Stockholm (Map, Lindstedtsvägen 28)

Organised by:
SeRC FLOW Community
Linné FLOW Centre
KCSE (KTH Computational Science and Engineering Centre)

High-performance computing platforms featuring million-way parallelism are coming online this summer and it is anticipated that exascale computers having billion-way concurrency will be deployed by 2018. In this talk, we explore fundamental computational complexity considerations that will drive algorithmic design choices for PDE-based simulation codes scaling to petascale and beyond.
Our focus is primarily on computational fluid dynamics. Our overall approach and analysis, however, is applicable to virtually any PDE-based physics problems that are addressed using grid-based discretizations coupled with domain-decomposition-based parallelism. We demonstrate the performance benefits of high-order numerical methods for simulations aimed at capturing multiscale phenomena in problems with a strong hyperbolic component. For elliptic problems (or substeps), we present analysis and performance results for scalable multigrid strategies that yield small iteration counts ( < 20 ) for systems comprising billions of unknowns.
In this context, we examine the potential future parallel scalability of PDE solvers, using explicit time steppers and multigrid as two bounding examples of approaches featuring local versus non-local interactions. We develop communication and work models based on measured performance data from leading-edge platforms over the past two decades to analyze these approaches and then apply these models to predict what exascale computation might enable. This analysis provides insight to design requirements of exascale algorithms, codes, and architectures.