# Speedup (1D FDTD)

**Speedup** compares parallel runtime with the time needed by the serial kernel for the same workload. If the serial runtime is $T_s$ and the runtime with $p$ OpenMP threads is $T_p$:

$$
S(p)=\frac{T_s}{T_p}
$$

A speedup of four means that parallel execution finishes in one quarter of the serial time. A value below one means that the OpenMP configuration is slower. The serial kernel is a separate execution mode; OpenMP with one thread still incurs parallel-region and synchronization overhead.

The plotting script takes the median serial runtime for each grid width and divides it by each parallel measurement. It then plots median speedups for each configuration. Comparisons assume that both modes use the same step count and simulation setup, as they do in the benchmark.

Ideal linear speedup would give $S(p)=p$. Actual results depend on serial source application, barriers, and the memory hierarchy. Some measurements can exceed linear speedup because cache behavior or processor frequency changes. [[fdtd-openmp-parallel-efficiency|Parallel efficiency]] expresses the measured speedup relative to the number of threads.