[petsc-users] Converting complex PDE to real for KNL performance ?

[Sajid Ali]

Hi Hong,

Apologies for creating unnecessary confusion by continuing the old thread
instead of creating a new one.

While I looked into converting the complex PDE formulation to a real valued
formulation in the past hoping for better performance, my concern now is
with TAO being incompatible with complex scalars. I would've preferred to
keep the complex PDE formulation as is (given that I spent some time tuning
it and it works well now) for cost function and gradient evaluation while
using TAO for the outer optimization loop.

Using TAO has the obvious benefit of defining a multi objective cost
function, parametrized as a fit to a series of measurements and a set of
regularizers while not having to explicitly worry about differentiating the
regularizer or have to think about implementing a good optimization scheme.
But if it converting the complex formulation to a real formulation would
mean a loss of well conditioned forward solve (and increase in solving time
itself), I was wondering if it would be better to keep the complex PDE
formulation and write an optimization loop in PETSc while defining the
regularizer via a cost integrand.

Thank You,
Sajid Ali | PhD Candidate
Applied Physics
Northwestern University
s-sajid-ali.github.io
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