CD_Solver

This will be a object-oriented PDE-solver, that allows one to solve a coupled nonlinear cross-diffusion system using the finite element software package ngsolve (https://ngsolve.org/). Using implicit Euler in time, finite element in space and Newton to overcoming nonlinearities.

Installation

• Install ngsolve by following the instruciton on https://ngsolve.org/.
• Install matplotlib (https://matplotlib.org/) and pandas (https://pandas.pydata.org/)
• Clone and change directory to CD_package:

$ git clone https://github.com/vjra/CD_Solver.git
$ cd CD_package

Introduction

Generates a experiment object to solve parabolic-parabolic system for $u=(\rho,c) \in \R^2$

$$u_t = \operatorname{div}(A(u) \nabla u) + f(u)$$

for t > 0 on a bounded domain Omega, with source term $f(u) = (0,-u[1]+u[0]^alpha)$ and parameters with $eps >= 0$ and $alpha >0$.

The experiment object builds on the ngsolve library and contains:

• the geometry,
• the mesh,
• the weak formulation of the problem,
• Test and Trial functions,
• simulation parameters,
• finite element space,
• initial data for the problem,
• solution of the computation as a ngsolve gridfunction.

Usage

See solve_example.py and plot_example.py for examples to solve and plot an experiment.