Advanced Topics from Scientific Computing

TU Berlin, Winter 2023/24

© Jürgen Fuhrmann .

Examination

Implementation of a particular PDE problem in Julia.

You will be able to use the VoronoiFVM.jl package I described in the lectures, but feel free to use other tools for the implementation, e.g. GridAP.jl or ExtendableFEM.jl by my colleague Christian Merdon. I would like to be able to check the running code.

Exam in groups up to three students

The exam is performed as a portfolio exam, up to three students can work together on a topic. The examination consists of

I will need this the day before your exam date.

Possible topics

Please feel free to ask me about a topic if you are interested, I will provide you with a write-up of the problem. Most of them are connected with some work I did earlier.

Nonlinear scalar problems:

∂tu−Δum=0\partial_t u - \Delta u^m =0 −∇ε∇u+eu−e−u=q-\nabla\varepsilon\nabla u + e^u - e^{-u}=q

Systems of equations:

{−∇k∇p=0∂tc−∇⋅(D∇c+ck∇p)=0 \begin{cases} -\nabla k\nabla p &=0\\ \partial_t c - \nabla \cdot (D\nabla c + c k \nabla p) &= 0 \end{cases} {∂tu1−∇D∇u1+r(u1,u2)=0∂tu2−∇D∇u2−r(u1,u2)=0 \begin{cases} \partial_t u_1 - \nabla D\nabla u_1 + r(u_1,u_2) &=0\\ \partial_t u_2 - \nabla D\nabla u_2 - r(u_1,u_2) &=0 \end{cases}

Your own choice:

© Jürgen Fuhrmann . Last modified: February 06, 2024. Website built with Franklin.jl and the Julia programming language.