Wednesdays 11:00am - 12:50pm
ONLINE
Office hours
TBD, or by appointment
The course will cover what are known as "fast solvers", algorithms for solving the linear systems arising from the discretization of elliptic PDEs.
The main textbook for the course is Martinsson, Fast Direct Solvers for Elliptic PDEs, 2019. The textbook is available for free (electronically) to NYU affiliates at siam.org.
The final grade in the course will be based on a course project and textbook presentations/discussions.
Below is an updated list of discussion topics along with any documents that were distributed, notes, or relevant code.
| Date | Topics | Materials |
|---|---|---|
| Sep 2 | Introduction to the course | Martinsson, Ch 1-2 Notes Recording |
| Sep 9 | NO CLASS | |
| Sep 16 | Low-rank approximation Randomized linear algebra |
Martinsson, Ch 3-4 Slides Recording |
| Sep 23 | Fast algorithms for rank-structured matrices | Martinsson, Ch 5 Slides Recording |
| Sep 30 | HODLR complexity The fast multipole method |
Martinsson, Ch 6 HODLR slides Notes Recording |
| Oct 7 | The fast multipole method | Martinsson, Ch 7-8 Notes Recording |
| Oct 14 | Integral equations: Continuous theory | Martinsson, Ch 10-11 Notes Recording |
| Oct 21 | Integral equations: discretization |
Martinsson, Ch 12 Notes Comments Recording |
| Oct 28 | FDS for IE: Multilevel scheme |
Martinsson, Ch 13-14 Notes Recording |
| Nov 4 | FDS for IE: HBS error estimation, ID, skeletonization | Martinsson, Ch 15-16 |
| Nov 11 | FDS for IE: Efficient compression |
Martinsson, Ch 17 Notes Recording |
| Nov 18 | FDS for IE: Scattering matrices |
Martinsson, Ch 18 Notes Recording |
| Nov 25 | FDS for PDE: Nested dissection |
Martinsson, Ch 19-20 Recording |
| Dec 2 | FDS for PDE: Fast sparse solvers |
Martinsson, Ch 21-22 Ch 21 slides Ch 22 slides Recording |
| Dec 9 | Project presentations | Recording |