2018 NCTS Short Course on

High-Performance Numerical Solvers

國家理論中心數學組 2017 秋季短期課程:高效能數值方法


Live Stream / Record


December 18-22, 25-29, 2017, and January 2-5, 2018 (Monday to Friday, 12:10-13:25)


Room 440, Astro-Mathematics Building, NTU (台灣大學 天文數學館 440室)


Edmond Chow Georgia Institute of Technology, USA http://www.cc.gatech.edu/~echow/Edmond Chow is an Associate Professor in the School of Computational Science and Engineering at Georgia Institute of Technology, USA. He previously held positions at D. E. Shaw Research and Lawrence Livermore National Laboratory. His research is in developing and applying numerical methods and high-performance computing to solve large-scale scientific computing problems and seeks to enable scientists and engineers to solve larger problems more efficiently using physical simulation. Specific interests include numerical linear algebra (preconditioning, multilevel methods, sparse matrix computations) and parallel methods for quantum chemistry, molecular dynamics, and Brownian/Stokesian dynamics. Dr. Chow earned an Honors B.A.Sc. in Systems Design Engineering from the University of Waterloo, Canada, in 1993, and a Ph.D. in Computer Science with a minor in Aerospace Engineering from the University of Minnesota in 1997. Dr. Chow was awarded the 2009 ACM Gordon Bell Prize and the 2002 U.S. Presidential Early Career Award for Scientists and Engineers (PECASE).

Course Overview

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).

Course Contents

    • 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



協辦單位:臺灣大學數學系與應用數學科學研究所台灣工業與應用數學學會 GPU與高效能計算活動學群

主持人:王偉仲 (台灣大學應數所),林文偉 (交通大學應數系),舒宇宸 (成功大學數學系),黃聰明 (台灣師範大學數學系)

聯絡人:游墨霏小姐 (02-3366-8814, murphyyu@ncts.ntu.edu.tw)