This is an OpenFOAM solver for the distributed control of the heat equation through the minimization problem
subject to the state equation
with and
.
The cost functional gradient is
where solves the adjoint problem
In the steepest descent method the cost gradient is used to update the control as
with sufficiently small.
The solver must be compiled in the terminal. It is advisable to first clean previous compilations with
wclean
and then use
wmake
OpenFOAM C++ library must be installed in order to compile the code.
The OpenFOAM distribution provided by the OpenFOAM Foundation was used.
In order to run the solver move to the case folder heatAdjoinFoamCase and type in the command line
./Allprepare
heatAdjointFoam
- The heatAdjointFoam solver has been tested in a square domain
with zero Dirichlet boundary conditions,
, and
,
,
. The target function is
.
- The heatAdjointFoam solver has been tested in a square domain
, and
,
. The target function is
.
It might be needed to use
sed -i -e 's/\r$//' filename
and
chmod +x filename
in order to be able to execute
./filename