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.

Lecture Time: Tu, Th 14:20--16:10
Location: 国科大中关村校区教学楼N108
Schedule:
  • Lecture 1 (09/03/2024): Introduction to linear solvers (slides0)
  • Lecture 2 (09/05/2024): Large-scale sparse systems
  • Lecture 3 (09/10/2024): Local approximation and relaxation (slides1)
  • Lecture 4 (09/12/2024): Linear stationary iterative methods (slides2)
  • Lecture 5 (09/19/2024): Basic ideas of multigrid (slides3)
  • Lecture 6 (09/24/2024): FEM and algebraic representations (slides4)
  • Lecture 7 (09/26/2024): Krylov subspace methods (slides5)
  • Lecture 8 (10/08/2024): Krylov subspace methods and preconditioning (slides6)
  • Lecture 9 (10/10/2024): Two-grid method, part 1 (slides7)
  • Lecture 10 (10/15/2024): Two-grid method, part 2
  • Lecture 11 (10/17/2024): Method of subspace corrections (slides8)
  • Lecture 12 (10/22/2024): Multilevel iterative methods, part 1 (slides9)
  • Lecture 13 (10/29/2024): Reynolds-robust multilevel solvers for incompressible flow (by P. Farrell, slides)
  • Lecture 14 (10/31/2024): Multilevel iterative methods, part 2
  • Lecture 15 (11/05/2024): Multilevel iterative methods, part 3 (slides10)
  • Lecture 16 (11/07/2024): Algebraic multigrid methods, part 1 (slides)
  • Lecture 17 (11/14/2024): Algebraic multigrid methods, part 2
  • Lecture 18 (11/19/2024): Robust iterative methods (slides)
  • Lecture 19 (11/28/2024): Resilient iterative methods (slides)
  • Lecture 20 (12/03/2024): Iterative methods to solve saddle point problems (by P. Devloo, slides)
  • Summary of the lectures (slides)


Lecture Notes (Updated on Nov/14/2024)