12:10~13:25, December 18, 2017 - January 5, 2018
Room 440, Astronomy-Mathematics Building, NTU
Speakers:
Edmond Chow (Georgia Institute of Technology)
Organizers:
Matthew M. Lin (National Cheng Kung University)
Tsung-Ming Huang (National Taiwan Normal University)
Weichung Wang (National Taiwan University)
Background & Purpose：
The mathematical development of modern numerical methods is intimately tied to high-performance computing, particularly for large-scale problems. This short course presents current ideas on high-performance numerical solvers, as well as foundational concepts necessary to understand the newest methods. The focus will be on numerical linear algebra and parallel computing techniques. Under consideration are parallel iterative solvers that avoid costly communication synchronization, hierarchical matrix representations for kernel-based problems and their relation to fast solvers, multigrid methods for solving extremely large problems in a scalable fashion, and other recent developments. This short course complements and extends the topics presented in the High-Performance Numerical Solvers short course taught in Summer 2016 (https://sites.google.com/site/school4scicomp/previous/2016-b-spring).
Topics
Krylov subspace methods
Projection method viewpoint and unifying framework
Specialized methods
Avoiding communication and synchronization
Restarting for eigenvalue solvers
Hierarchical matrix methods
Physical intuition and relation to fast multipole methods
Hierarchical matrix construction and solution methods
Domain decomposition methods
Optimized Schwarz methods
FETI and related methods
Multigrid methods
Convergence theory
Algebraic multigrid
Parallel Preconditioning
Advanced ideas on incomplete factorizations
Advanced ideas on sparse approximate inverses
Other recent developments