PETSc: OMP+MKL in MatShell

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I am trying to use a custom matvec operator with PETSc MatShell in Fortran and inside of it, I want to use a mix of OpenMP and MKL multithreading (blas).

The OpenMP and MKL threads are indeed launched, but htop shows that only the OpenMP threads occupy 200% of the CPU (2 threads at 100%) when there are 48 cores available.

I can indeed see the rest of the threads (MKL) on htop but they use 0% of CPU.

How can I achieve this?

Edit: I'm glad to post more details. I'm shooting for a short message first in case someone has run into the same issue.

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