Fast Solvers for Large Algebraic Systems
Computational modeling is the “third paradigm” of scientific discovery, alongside theory and experiment. Researchers use computational simulation to gain new scientific insights and seek technological innovations. Most of the problems of interest are described by several nonlinear models and large systems of equations. This lecture series gives you insight into the latest advances in large-scale simulation techniques, with a focus on algebraic solution methods. Reflecting the latest research developments in the field, the lectures will guide you in developing and using efficient solvers for large-scale distributed simulation.
Regular Lectures:
- Lecture 0: Introduction (Slides)
- Lecture 1: Large-scale numerical simulation (Slides, Homework)
- Lecture 2: Fast solvers for sparse linear systems (Slides, Homework, Reorderings)
- Lecture 3: Methods for non-symmetric problems (Slides, Homework)
- Lecture 4: Methods for nonlinear problems (Slides, Homework)
- Lecture 5: Mixed-precision methods (Slides, Homework)
- Lecture 6: Communication hiding and avoiding (Slides, Homework)
- Lecture 7: Fault resilience and reliability (Slides, Homework)
- Lecture 8: Robustness and adaptivity (Slides, Homework)
- Final project dues on July 15 2022
Special Topics:
Besides the regular lectures, there will be five special talks on various related topics, including sparse numerical linear algebra, finite element discretization, eigenvalue solvers, performance optimization, and real applications. These special lectures are carefully designed to help the audiences to get a more complete picture on numerical simulation.
- Topic 1: Optimization of Sparse Basic Linear Algebra Subroutines (June 19, by Prof. Dr. Weifeng Liu, CUP Beijing, Slides)
- Topic 2: Lagrange Finite Element Programming on Simplex Meshes (June 25, by Prof. Dr. Huayi Wei, XTU, Slides)
- Topic 3: Augmented Subspace Method for Eigenvalue and Nonlinear Problems (June 26, by Prof. Dr. Hehu Xie, AMSS, Slides)
- Topic 4: An Introduction to Performance Analysis and Modeling of Parallel Programs (July 02, by Prof. Dr. Wei Xue, Tsinghua, Slides)
- Topic 5: Sparse Linear Solvers: How Far We Are From Large-Scale Real Applications (July 03, by Prof. Dr. Xiaowen Xu, IAPCM, Slides)
Time: June 18, 19, 25, 26 and July 02, 03, 10, 13:30--17:30 (Beijing Time)
Location: Tencent Webniar
Recorded lectures on bilibili!
Poster: download