2020-A-Nakajima Kengo

Parallel Finite Element Method using Supercomputer

February 21-25, 2020

Room 102, Astro-Mathematics Building, National Taiwan University

Announcements

請在 2019/01/29 17:00 前線上註冊 : https://forms.gle/BTmSA1Kh5Zsmfghp7

(本課程名額有限，錄取學員將另行通知。)

Overview

This 5-day intensive class provides introduction to large-scale scientific computing using the most advanced massively parallel supercomputers. Topics cover:

  • Finite-Element Method (FEM)

  • Message Passing Interface (MPI)

  • Parallel FEM using MPI and OpenMP

  • Parallel Numerical Algorithms for Iterative Linear Solvers

Several sample programs will be provided and participants can review the contents of lectures through hands-on-exercise/practices using the Oakbridge-CX system at the University of Tokyo (https://www.cc.u-tokyo.ac.jp/en/supercomputer/obcx/service/).

Finite-Element Method is widely-used for solving various types of real-world scientific and engineering problems, such as structural analysis, fluid dynamics, electromagnetics, and etc. This lecture course provides brief introduction to procedures of FEM for 1D/3D steady-state heat conduction problems with iterative linear solvers and to parallel FEM. Lectures for parallel FEM will be focused on design of data structure for distributed local mesh files, which is the key issue for efficient parallel FEM. Introduction to MPI (Message Passing Interface), which is widely used method as "de facto standard" of parallel programming, is also provided.

Solving large-scale linear equations with sparse coefficient matrices is the most expensive and important part of FEM and other methods for scientific computing, such as Finite-Difference Method (FDM) and Finite-Volume Method (FVM). Recently, families of Krylov iterative solvers are widely used for this process. In this class, details of implementations of parallel Krylov iterative methods are provided along with parallel FEM.

Moreover, lectures on programming for multicore architectures will be also given along with brief introduction to OpenMP and OpenMP/MPI Hybrid Parallel Programming Model.

Students from the universities that have agreements with NCTS (National Center for Theoretical Sciences) can obtain TWO credits after completion of this course. The universities include NTU, NTHU, NCTU, NCKU, NCCU, NCU, CCU, NCHU, NSYSU, NDHU, SCU, TKU, and NUK.

Schedule

February 21, 2020 (Fri 9:10-17:30)

09:10-10:00 Introduction (1/2)

10:10-11:00 Introduction (2/2)

11:10-12:00 FEM (1/6)

13:10-14:00 FEM (2/6)

14:10-15:00 FEM (3/6)

15:10-16:00 FEM (4/6)

16:10-17:30 Exercise (Optional)

February 22, 2020 (Sat 9:10-17:30)

09:10-10:00 FEM (5/6)

10:10-11:00 FEM (6/6)

11:10-12:00 Exercise

13:10-14:00 Parallel FEM

14:10-15:00 Login to OBCX

15:10-16:00 MPI (1/6)

16:10-17:30 Exercise (Optional)

February 23, 2020 (Sun 9:10-17:30)

09:10-10:00 MPI (2/6)

10:10-11:00 MPI (3/6)

11:10-12:00 Exercise

13:10-14:00 MPI Practice (1/3)

14:10-15:00 MPI (4/6)

15:10-16:00 MPI (5/6)

16:10-17:30 Exercise (Optional)


February 24, 2020 (Mon 9:10-17:30)

09:10-10:00 MPI (6/6)

10:10-11:00 Exercise

11:10-12:00 Exercise

13:10-14:00 MPI Practice (2/3)

14:10-15:00 MPI Practice (3/3)

15:10-16:00 Exercise

16:10-17:30 Parallel FEM (1/4)

February 25, 2020 (Tue 9:10-17:30)

09:10-10:00 Parallel FEM (2/4)

10:10-11:00 Parallel FEM (3/4)

11:10-12:00 Parallel FEM (4/4)

13:10-14:00 Exercise

14:10-15:00 OpenMP/MPI Hybrid (1/2)

15:10-16:00 OpenMP/MPI Hybrid (2/2)

16:10-17:30 Exercise (Optional)

Prerequisites

  • Experiences in Unix/Linux (vi or emacs)

  • Experiences in programming by Fortran or C/C++

  • Undergraduate-Level Mathematics and Physics (e.g. Linear Algebra, calculus)

  • Fundamental numerical algorithms (Gaussian Elimination, LU Factorization, Jacobi/Gauss-Seidel/SOR Iterative Solvers, Conjugate Gradient Method (CG))

  • Experiences in SSH Public Key Authentication Method (optional)

  • Participants are encouraged to read the following material, and to understand fundamental issues of the MWR (Method of Weighted Residual) before this course. http://nkl.cc.u-tokyo.ac.jp/19w/02-FEM/FEMintro.pdf

Preparation for PC

  • Windows

    • Cygwin with gcc/gfortran and OpenSSH

      • Please make sure to install gcc (C) or gfortran (Fortran) in “Devel”, and OpenSSH in “Net”

    • ParaView

  • MacOS, UNIX/Linux

    • ParaView

  • Cygwin: https://www.cygwin.com/

  • ParaView: http://www.paraview.org

Instructor

Prof. Kengo Nakajima

Information Technology Center, The University of Tokyo, Tokyo, Japan [Web]

Additional Materials

主辦單位：科技部 國家理論科學研究中心數學組

協辦單位：東京大學情報基盤中心，科技部人工智慧技術暨全幅健康照護聯合研究中心，台灣工業與應用數學學會，臺灣大學數學系與應用數學科學研究所

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：劉馥瑤小姐 (02-3366-8819, medalab.contact@gmail.com), Medical Data Analytics Laboratory (MeDA Lab, http://meda.ai)