steady-2d-heat-inverse

1. Solve the 2D steady-state heat equation.
2. Solve the inverse problem to infer the position-dependent thermal conductivity

Installation

With conda/mamba and pip:

conda env create -n steady-2d-heat-inverse -f environment.yml
conda activate steady-2d-heat-inverse
pip install -e .

Usage

• The notebooks/ForwardSolve.ipynb notebook demonstrates how to solve the forward problem.
• The notebooks/InverseSolve.ipynb notebook demonstrates how to solve the inverse problem.

Tests

To run gradient tests:

pytest -m gradcheck

References

• [1] Hans P. Langtangen and Kent-Andre Mardal, "Introduction to Numerical Methods for Variational Problems"
• [2] Hans P. Langtangen and Anders Logg (adapted by Jørgen S. Dokken) "The FEniCS tutorial"
• [3] Hans P. Langtangen, "Approximation of Functions"
• [4] Andrew M. Bradley, "PDE-constrained optimization and the adjoint method"