Utilizing machine topology in numerical algorithms Luke Olson - PowerPoint PPT Presentation

Utilizing machine topology in numerical algorithms Luke Olson Department of Computer Science Computational Science and Engineering University of Illinois at Urbana-Champaign


 
 
 Overview • I use Blue Waters to solve large sparse linear systems and to study the performance 
 [ ][][] A b x = • Why? Time step other Linearization Assembly solve Solve Adapt Image: David Keyes??

Application: Plasma-coupled Combustion • The Center for Exascale Simulation of Plasma-Coupled Combustion XPACC @ Illinois Oxidizer Fuel O - Ar; Air H ; CH 2 2 4

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 • Electric conductivity influences the electric field and current density over time r · σ r r φ = g


 
 
 
 
 
 
 
 Application: Plasma-coupled Combustion • The Center for Exascale Simulation of Plasma-Coupled Combustion @ Illinois 
 XPACC • Electric field a key element in the plasma arc • 30+ meshes Image credit: Kyle Mckay @ Illinois (joining LLNL) •

Why Blue Waters? • Sparse matrix operations are communication dominant — performance models play a key role. • Exploiting machine layout plays an important role in addressing bottlenecks in communication. • Blue Waters has enabled us to develop/test/scales codes to address these issues Structured Multigrid Algebraic Multigrid

Sparsity (a.k.a. data relationships )