Performance Index (PID)

Performance Index (PID)

The performance index is a measure to judge the computational efficiency of a CFD solver. It expresses the computational time required to update one degree of freedom for one runge kutta step, i.e.

\begin{equation} PID = \frac{t_{wall} \cdot np \cdot nThreads}{nDOF \cdot nTimeSteps \cdot nRungeKuttaStages}. \end{equation}

Here, \(t_{wall}\) is the wall clock time in seconds, \(np\) is the number of mpi ranks, \(nThreads\) is the number of threads, \(nDof\) is the number of degrees of freedom, \(nTimeSteps\) is the number of time steps between each PID-output and \(nRungeKuttaStages\) is the number of stages in the Runge-Kutta scheme.

Typically, the PID ranges between \(1-10 \mu s\) depending on several factors such as the chosen solver mode, efficiency of the splitting, current architecture etc.