Choosing the right parameter for scaling is very important for deciding relative performance between processors. In the grid solver if we choose to increase the size of the grid, we are also increase the time taken for convergence by a factor of O(N). Essentially by increase the size of grid by O(N) in one dimension, we have increased the processing time by O(N^3). If we assume that our increase is linear and just also increase the processors linearly, the performance will sub-optimal, because this nature is inherent by design of our problem.
yeq
Another example that altering parameters could be tricky is that if we increase the total time T to calculate the simulation, though the problem becomes larger, it does not affect the way the program is parallelized because this parameter is only sequential-dependent.
Choosing the right parameter for scaling is very important for deciding relative performance between processors. In the grid solver if we choose to increase the size of the grid, we are also increase the time taken for convergence by a factor of O(N). Essentially by increase the size of grid by O(N) in one dimension, we have increased the processing time by O(N^3). If we assume that our increase is linear and just also increase the processors linearly, the performance will sub-optimal, because this nature is inherent by design of our problem.
Another example that altering parameters could be tricky is that if we increase the total time T to calculate the simulation, though the problem becomes larger, it does not affect the way the program is parallelized because this parameter is only sequential-dependent.