ENH: avoid the build-up of the background solver dictionary

The solverPerformanceDict gets larger due to the addition of a SolverPerformance
data per field at every outer iteration within the same main iteration/time
step.

However, the subsequent functionalities seem to use only the first and last
element of this dictionary per field; therefore, storing the interim values
was revealed to be redundant.

The change removes the interim values by transforming the `List` container
into the `Pair` container, and modifying the relevant algorithms.