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.

Regular time: Friday 9:00am--11:30am
Location: N202, AMSS

  • Lecture 1 (Sep/02/2016): Introduction
  • Lecture 2 (Sep/09/2016): Iterative methods; HW: 2.2, 2.3, 2.6, 2.7
  • Lecture 3 (Sep/23/2016): Domain decomposition method
  • Lecture 4 (Sep/30/2016): Two-grid method; HW: 3.2, 3.3, 3.4, 3.6
  • Lecture 5 (Oct/14/2016): Method of subspace corrections 1
  • Lecture 6 (Oct/21/2016): Method of subspace corrections 2
  • Lecture 7 (Oct/28/2016): Applications of MSC; HW 4.2, 4.5
  • Lecture 8 (Oct/31/2016): AMG methods I--Prof. J. Xu (PSU), S Hall, 8:30am--11:30am
  • Lecture 9 (Nov/01/2016): AMG methods II--Prof. J. Xu (PSU), N219, 8:30am--12:00pm
  • Lecture 10 (Nov/02/2016): AMG methods III--Prof. J. Xu (PSU), N219, 8:30am--12:00pm
  • Lecture 11 (Nov/03/2016): AMG methods IV--Prof. J. Xu (PSU), N219, 8:30am--12:00pm
  • Lecture 12 (Nov/04/2016): AMG methods V--Prof. J. Xu (PSU), N219, 8:30am--11:30am
  • Lecture 13 (Nov/18/2016): Solvers for nearly-singular problems--Prof. J. Wu (PKU)
  • Lecture 15 (Nov/25/2016): HB and BPX methods
  • Lecture 16 (Dec/02/2016): Solvers for fourth-order problems--Dr. S. Zhang (LSEC)
  • Lecture 17 (Dec/09/2016): Multigrid methods, N514
  • Lecture 18 (Dec/23/2016): Applications of multilevel solvers
  • Final project (Dec/16/2016): Discussion on final project, Z210, 10:00am--12:00pm

Course Syllabus
Lecture note (version 2016.12.31, Chapter 8 has not been finished)