1D Compute-to-Communicate Ratio
Intracore computing Intercore communication
Compute : Communicate ratio = N : 2

where N is the number of compute cells per core
Computer Graphics
In the above drawing, Compute : Communicate is 4 : 2
mjb – June 12, 2021
Computer Graphics
The Compute : Communicate Ratio

compute_communicate_ratio.pptx
mjb – June 12, 2021
How do more Cores Interact with the Compute-to-Communicate Ratio?
In this case, with 4 cores, Compute : Communicate = 4 : 2
In this case, with 8 cores, Compute : Communicate = 2 : 2
Think if it as a Goldilocks and the Three Bears sort of thing. 🙂
Too little Compute : Communicate and you are spending all your time
sharing data values across threads and doing too little computing
Too much Compute : Communicate and you are not spreading out your problem among enough threads to get good parallelism.
Computer Graphics
It’s difficult to find the “sweet spot” without running experiments
mjb – June 12, 20
Performance as a Function of Number of Nodes 4
Computer Graphics
# of Nodes to Compute # of Threads
mjb – June 12, 2021
Performance as a Function of Number of Threads 5
Computer Graphics
# of Nodes
mjb – June 12, 2021
CT k(2T 2T)
 k Ti1,j 2Ti,j Ti1,j Ti,j 
T k 2T 2T
 C  x2
2D Heat Transfer Equation
Ti,j1 2Ti,j Ti,j1  t
tC(x2 y2)
Computer Graphics
mjb – June 12, 2021
MegaNodes Computed Per Second
MegaNodes Computed Per Second

Computer Graphics
Area-to-Perimeter
2D Compute-to-Communicate Ratio
Intracore computing Intercore communication
Compute : Communicate ratio = N2 : 4N = N : 4
where N is the dimension of compute nodes per core
The 2D Compute : Communicate ratio is sometimes referred to as
mjb – June 12, 2021
T 2T 2T 2T C t k(x2  y2  z2 )
 k T 2T T T 2T T T 2T T 
 i1,j,k i,j,k i1,j,k  i,j1,k i,j,k i,j1,k  i,j,k1 i,j,k i,j,k1t
3D Heat Transfer Equation
 C  x y 
T k 2T 2T 2T tC(x2 y2 z2)
Computer Graphics
mjb – June 12, 2021
3D Compute-to-Communicate Ratio
Compute : Communicate ratio = N3 : 6N2 = N : 6
where N is the dimension of compute nodes per core
In 3D the Compute : Communicate ratio is sometimes referred to as
Volume-to-Surface
Computer Graphics
mjb – June 12, 2021