Fast PDE/IE course, Skoltech, Spring 2015


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

  1. We will try to use Python and IPython/Jupyter notebooks for everything (lecture notes & homework assignments)
  2. I highly recommend you to install Anaconda Python Distribution
    (Skoltech email is enough for the free Academic license for the full version)
  3. Python 2.7 is used
  4. 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


  • 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


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


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


Now let us start the First lecture

In [1]:
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