CSE III: Fast & efficient solvers, Skoltech, Fall 2017

Team

Ivan Oseledets, Associate Professor, Skoltech

Maxim Rakhuba, TA
Alexander Katrutsa, TA
Alexey Boyko, TA

How do we grade

40% homework (3 problem sets + 1 project proposal)
30% Oral exam
30% Application period (term project)

Late submissions within 2 days are graded up to 80% of the total score. 50% penalty is applied if you submit even later.

Details are in rules!

Technical details

We will use Python 3 and Jupyter notebooks for everything (lecture notes & homework assignments)
I highly recommend you to install Anaconda Python Distribution
Feel free to ask TAs for help

Course description

PDE (Partial differential equations) and IE (integral equations) are the barebones for physical simulations.

We will discuss how to solve them, and how to solve them fast.

We will also give an overview of state-of-the art technique for solving PDEs and IEs even faster.

Learning outcomes

Fast methods for integral equations (convolutions, FFT, fast multipole method)
Fast methods for PDEs (advanced sparse solvers, multigrid methods, domain decomposition)
Fast solvers by advanced discretization (isogeometric analysis, hp, QTT)
Fast solvers for parametric problems (model order reduction, $N$-term approximation)

Syllabus

Week 1: Intro & basic integral equations (turning PDEs into IEs, typical kernels, Nystrom, collocation, Galerkin, quadrature for singular/hypersingular integrals).
Week 2: Translation-invariant kernels and convolutions, FFT. Concept of close and far interactions, precorrected FFT. Barnes-Hut method. Fast multipole method.
Week 3: Finite difference/finite element/finite volume: discretization & packages. Basic and advanced sparse solvers.
Week 4: Geometric multigrid method. Black-box multigrid method. Algebraic multigrid method. Domain decomposition method.
Week 5: Fast solvers by advanced discretization methods: basic concepts of isogeometric analysis, hp-discretization, wavelet approximation, tensor approximation.
Week 6: Solvers for parametric problems: model order reduction, polynomial approximation, best $N$-term approximation
Week 7-8: Oral exam, projects

Homework

3 problem sets + 1 project proposal

Oral exam

Week 7

Projects

Week 8
Submit project proposal according to the proposal form
You will be splitted in teams by instructors and then will be able to choose the project

Materials

Lecture notes
Bother TAs with questions
We will point out important books/papers when appropriate

Starting

Now let us start the First lecture



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