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 10:00am--11:30am
Location: N308 (中关村校区教学楼)
Schedule:
- Lecture 1 (03/07/2023): Introduction
- Lecture 2 (03/14/2023): Local approximation
- Lecture 3 (03/16/2023): Stationary iterative methods
- Lecture 4 (03/21/2023): Krylov subspace methods, part 1
- Lecture 5 (03/23/2023): Krylov subspace methods, part 2
- Lecture 6 (03/28/2023): Preconditioning methods
- Lecture 7 (03/30/2023): FEM and algebraic representations
- Lecture 8 (04/04/2023): Smoothing effect
- Lecture 9 (04/06/2023): Exact twogrid methods
- Lecture 10 (04/11/2023): Inexact twogrid methods (by Xuefeng Xu)
- Lecture 11 (04/13/2023): From twogrid to multigrid (by Xuefeng Xu)
- Lecture 12 (04/18/2023): Method of subspace corrections
- Lecture 13 (04/20/2023): The XZ identity
- Lecture 14 (04/25/2023): Parallel subspace correction methods, part 1
- Lecture 15 (04/27/2023): Parallel subspace correction methods, part 2
- Lecture 16 (05/04/2023): Geometric multigrid methods
- Lecture 17 (05/09/2023): Implementation of multigrid methods
- Lecture 18 (05/11/2023): Algebraic multigrid methods, part 1
- Lecture 19 (05/16/2023): MSC for nearly singular problems (by Youngju Lee)
- Lecture 20 (05/18/2023): Algebraic multigrid methods, part 2
Lecture Notes (Updated on May/15/2023)