Scientific Computing

TU Berlin, Winter 2020/21

© Jürgen Fuhrmann .

Project Based Exam

This is the variant close to my initial plan

Implementation of a particular 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. I would like to be able to check the running code.

I will deliver two more items to start this:

Write a short report about the implementation

Possible topics.

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

Nonlinear scalar problems:

∂tu−Δum=0\partial_t u - \Delta u^m =0 ∂ts(u)−∇⋅k(u)∇u=0\partial_t s(u) - \nabla\cdot k(u)\nabla u=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: March 02, 2021. Website built with Franklin.jl and the Julia programming language.