I have had a lot of fun and some heart ache playing with the MKL Library and the PARDISO solver.
The PARDISO solver is very fast. The problem I am solving is the hydraulic network problem, in this case using the Gradient Method. The PARDISO solver gives a much better first estimate of the solution vector, which can be measured using the error on the sum of the hydraulic heads. It's first pass gives a 4 fold better estimate than the other solvers (all that I have tried).
But the solver then converges very slowly to the "best estimate" of the answer, taking 8000 iterations to do what the others do in 20. So the fact that the iterations are fast, is lost in the slow convergence.
I have played with passing the A array into the PARDISO solver in different formats, both the sparse and the dense matrix, it makes no difference. Rum really. I look step by step at the solution vector, and it is a long way from the other inversion solution vector even on the first iteration for the fully dense solvers.
Interestingly if I run as a PHASE 33 - I get errors, but it works, if I use 13 - it also works slowly, but I do not get the errors.
It does solve, but it is not faster in the end than the other solvers, interesting really.
Question: Should I try another MKL solver?
JMN