AD implementation for custom topology optimization variables (gammaDV → Helmholtz filter → projection → alpha)

[Ananth-Narayan-IITM]

Hi everyone,

I am implementing density-based topology optimization in DAFoam and I am having difficulty understanding how a new chain of variables should be incorporated into the AD framework.

gammaDV (design variable) -> Helmholtz filter -> gammaFilter -> Projection -> gamma -> 

-> Brinkman interpolation -> alpha -> Momentum equation and  Objective / Constraints

The filter equation is

fvScalarMatrix gammaFilterEqn
(
    -fvm::laplacian(pow(radius,2), gammaFilter)
  + fvm::Sp(oneGammaFilter, gammaFilter)
 == gammaDV
);

gammaFilterEqn.solve();

followed by the projection and Brinkman interpolation to compute alpha.

I inspected DASimpleFoam, observed that CoDiPack is typically used as

globalADTape_.reset();
globalADTape_.setActive();

registerInput(...);

// compute operator

setPassive();

evaluate(...);

However, I am not sure whether my filter/projection chain should be implemented using this approach.

I am unsure what is the correct architecture for introducing a new design-variable chain into DAFoam. Should I tape the entire chain, I am very unclear on how to proceed

Ultimately I need derivatives such as d(Objective)/d(gammaDV) and d(VolumeConstraint)/d(gammaDV), where the objective or constraint depends directly on gamma or alpha.

Could someone point me to the recommended way of implementing this within DAFoam's AD framework?

Any guidance or relevant examples would be greatly appreciated.

Thank you