examples: Enhance MPI notebook with paper material #7179

Job	Run time
pytest-ubuntu-py311-gcc11-noomp-base	28m 48s
pytest-ubuntu-py311-gcc11-noomp-adjoint	28m 48s
pytest-ubuntu-py312-gcc12-omp-base	28m 48s
pytest-ubuntu-py312-gcc12-omp-adjoint	28m 47s
pytest-ubuntu-py39-gcc7-omp-base	28m 48s
pytest-ubuntu-py39-gcc7-omp-adjoint	29m 37s
pytest-ubuntu-py310-gcc10-noomp-base	28m 50s
pytest-ubuntu-py310-gcc10-noomp-adjoint	28m 50s
pytest-ubuntu-py312-gcc13-omp-base	29m 36s
pytest-ubuntu-py312-gcc13-omp-adjoint	29m 37s
pytest-ubuntu-py39-gcc9-omp-base	29m 36s
pytest-ubuntu-py39-gcc9-omp-adjoint	28m 48s
pytest-osx-py312-clang-omp-base	29m 39s
pytest-docker-py39-gcc-omp-base	29m 38s
pytest-docker-py39-gcc-omp-adjoint	28m 49s
pytest-docker-py39-icx-omp-base	29m 39s
pytest-docker-py39-icx-omp-adjoint	28m 49s
	8h 15m 27s

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