General Speed Up and Efficiency Analysis II
In many problems there is an elegant formula fcomm = constant . tcomm/(n1/d tfloat)
d is system information dimension which is equal to geometric dimension in problems like Jacobi where communication is a surface and calculation a volume effect
- We will see soon case where d is NOT geometric dimension
d=1 for Hadrian’s wall and d=2 for Hadrian’s Palace floor while for Jacobi in 1 2 or 3 dimensions, d =1 2 or 3
Note formula only depend on local node and communication parameters and this implies that parallel computing does scale to large P if you build fast enough networks (tcomm/tfloat) and have a large enough problem (big n)