Interior Control of the Poisson Equation with the Steepest Descent Method in OpenFOAM
In this work we solve the optimal control problem
We use the steepest descent method based on the adjoint methodology. The corresponding adjoint system writes as
The directional derivative of the cost function is given by
and the control variable is updated according to
The solver must be compiled in the terminal. It is advisable to first clean previous compilations with
and then use
OpenFOAM C++ library must be installed in order to compile the code.
The OpenFOAM distribution provided by the OpenFOAM Foundation was used.
Running a Case
In order to run the solver move to the case folder poissonAdjoinFoamCase and type in the command line
It might be needed to use
sed -i -e 's/\r$//' filename
chmod +x filename
in order to be able to execute
- Jose Lorenzo Gomez
- Víctor Hernández-Santamaría
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 694126-DyCon).
- F. Tröltzsch. Optimal control of partial differential equations: theory, methods, and applications. American Mathematical Soc., 2010.