Hello all,
I am experimenting with the Fenics finite element software for solving the time-harmonic Maxwell system for electromagnetic wave propagation problems. The benefit of the least squares approach is the self-adjointedness of the finite element operators that permits the use of efficient conjugate gradient solvers for very large problems using simple preconditioners (Jacobi, SOR).
The problem is that the least squares formulation suffers from non-physical loss as a result of truncation error (I suspect) in the differential operators.
I would be very interested to share experiences with people out there who have experimented with this approach in electromagnetics or fluid dynamics.
A more complete description of what I am doing can be found in the discussion on the Fenics Discourse site here: https://fenicsproject.discourse.group/t/least-squares-finite-element-formulations-for-time-harmonic-electromagnetic-fields/2024
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