Fast PDE/IE course, Skoltech, Spring 2015

Team

Ivan Oseledets, Associate Professor, Skoltech
Alexander Shapeev, Assistant Professor, Skoltech
Maxim Rakhuba, TA
Evgeny Frolov, TA
Dasha Sushnikova, TA
Artem Naumov, TA

How do we grade

50% homework
20% 2 written tests
30% Application Period
pass-fail ping-pong test

Strict deadlines with 5 days of additional budget. 50% max for late submissions

Attendance control not strict

(as usual do not disappoint us: the negative bonus can be large)

Technical details

We will try to use Python and IPython/Jupyter notebooks for everything (lecture notes & homework assignments)
I highly recommend you to install Anaconda Python Distribution
(Skoltech email is enough for the free Academic license for the full version)
Python 2.7 is used
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.

Learning outcomes

Finite elements & meshes for elliptic & parabolic problems
Sparse linear systems (direct solvers, preconditioners, multigrid)
Software packages for solving PDEs
Basic integral equations for exterior problems
High-frequency problems & convolution & FFT

(Approximate) Syllabus

Week 1: Physical models & PDE & IE, finite differences 1D/2D
Week 2: FEM (basic elements, meshes, tools for meshing)
Week 3: Sparse matrices/iterative methods/multigrid (geom & AMG)
Week 4: Exterior problems & IE: discretization, quadrature, multipole, hierarchical matrices + test)
Week 5: High-frequency & Fourier
Week 6: Software packages for PDEs
Week 7: Exam & test
Week 8: App Period

Homework

4 problem sets
Each Friday (starting from the week 2) will be the deadline
Everybody has a resource of 5 days to postpone problem sets deadlines

Tests

2 written tests (week 4 and week 7)
Ping-pong test (week 7)

Materials

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

Starting

Now let us start the First lecture



In [1]:

    
from IPython.core.display import HTML
def css_styling():
    styles = open("./styles/custom.css", "r").read()
    return HTML(styles)
css_styling()









    Out[1]: