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Taiwan Mathematics School: HPC for Tomorrow-High-Performance Numerical Solvers
December 18, 2017 to January 5, 2018, December 18, 2017 - January 5, 2018

Edmond Chow (Georgia Institute of Technology)

Matthew M. Lin (National Cheng Kung University)
Tsung-Ming Huang (National Taiwan Normal University)
Weichung Wang (National Taiwan University)

Astro-Mathematics Building, National Taiwan University
Course Description: 
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.

o    Krylov subspace methods

§  Projection method viewpoint and unifying framework

§  Specialized methods

§  Avoiding communication and synchronization

§  Restarting for eigenvalue solvers

o    Hierarchical matrix methods

§  Physical intuition and relation to fast multipole methods

§  Hierarchical matrix construction and solution methods

o    Domain decomposition methods

§  Optimized Schwarz methods

§  FETI and related methods

o    Multigrid methods

§  Convergence theory

§  Algebraic multigrid

o    Parallel Preconditioning

§  Advanced ideas on incomplete factorizations

§  Advanced ideas on sparse approximate inverses

§  Other recent developments


Contact: Murphy Yu, murphyyu@ncts.ntu.edu.tw, 02-3366-8814

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