Scalable High Performance Libraries in Linear Algebra
Kinds of Problems, Algorithms, and Parallelism
Why Are We Still Doing This?
The Importance of Exploiting Mathematical Structure
Changing Algorithmic Approach
Software Technology & Performance
Different Architectures
High-Performance Computing Directions
Performance Issues - Cache & Bandwidth
Where Do the Flops Go? Memory Hierarchy
BLAS for Performance
How To Get Performance From Commodity Processors?
Code Generation Strategy
ATLAS 500x500 DGEMM Across Various Architectures
Recursive Approach for Other Level 3 BLAS
500x500 Recursive BLAS on 433Mhz DEC 21164
LAPACK
ScaLAPACK For Distributed Memory
Choosing a Data Distribution
Possible Data Layouts
New Algorithms/Software
Parallelism in ScaLAPACK
ScaLAPACK - What’s Included?
Heterogeneous Computing
Sparse Direct Methods
Example: Super-LU X.S. Li and J. Demmel,UCB
Sparse Gaussian Elimination
Many Sparse Direct Solvers
Iterative Solvers - Krylov Subspace Methods
Decision Tree
Iterative Solvers
Three Good Starting Places
DOE ASCI Program: Stockpile Stewardship via Numerical Simulation and Non-nuclear Experiments
Application needs drive the platforms and software infrastructure development
ASCI is Developing Application Codes that Scale to Thousands of Processors
Scalable Algorithms are the Key to Terascale Simulation
Multigrid for Scalable Solvers
Numerical Libraries
Research Directions
Conclusions
Thanks to…
Email: dongarra@cs.utk.edu
Home Page: http://www.netlib.org/utk/people/JackDongarra/