Introduction to Multilevel Iterative Methods

Over the last few decades, intensive research has been done on developing efficient parallel iterative solvers for PDEs. One useful mathematical technique that has drawn a lot of attention is multilevel iterative solvers and preconditioners. In this seminar series, we will discuss development of multilevel iterative solvers for solving partial differential equations. The format of this seminar is a mixed of blackboard-based lectures on fundamentals and talks on more advanced research topics.

Time: Wed 10:00am--11:45am
Location: Jiao Xue Lou N308, Zhongguancun District, UCAS (中科院大学中关村校区教学楼N308)

  • Lecture 1 (Sep/12/2018): Introduction; HW1: 1.5
  • Lecture 2 (Sep/19/2018): Iterative methods; HW1: 2.1, 2.5
  • Lecture 3 (Sep/26/2018): Preconditioning and DDM; HW1: 2.8, 2.9
  • Lecture 4 (Oct/10/2018): Matrix representation
  • Lecture 5 (Oct/17/2018): Two-grid methods; HW2: 3.5, 3.6
  • Lecture 6 (Oct/24/2018): Method of subspace corrections 1; HW2: 4.3, 4.4
  • Lecture 7 (Oct/31/2018): Method of subspace corrections 2
  • Lecture 8 (Nov/07/2018): HB preconditioner
  • Lecture 9 (Nov/21/2018): BPX preconditioner; HW3: 5.1, 5.2, 5.3
  • Lecture 10 (Nov/28/2018): Geometric multigrid method
  • Lecture 11 (Dec/05/2018): Algebraic multigrid method

Course Syllabus
Lecture note (version 2018.12.05)
Reference solution to homework (version 2018.12.05)
Final project (version 2018.11.1, due on 2018.12.15)