Data Local Iterative Methods For The Efficient Solution of Partial Differential Equations

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rb1.F Program Description

File Name:

rb1.F

Description:

Uses standard (5-point stencil) way to do the Red-Black Gauss-Seidel method. It performs one complete sweep of the grid from bottom to top updating all the red nodes and then one complete sweep updating all the black nodes.

Comment:

The sweep through the grip updating all the black nodes reuses all nodes touched by the update of the red nodes. Assuming that the whole grid does not fit in the cache, the data of the lower part of the grid is no longer in the cache after the red update sweep because the data was replaced by the grid points in the upper part of the grid. Hence, the data must be loaded from slower main memory into the cache again. Doing this they replace the upper part of the grid points in the cache and as a consequence they have to be loaded from main memory once more. If several Red-Black Gauss-Seidel sweeps are performed consecutively the same also applies to the red update sweep.

Results:

Memory access behaviour
Size	MBytes /sec	% of all access which go into
Size	MBytes /sec	±	1. Level	2. Level	3. Level	Memory
32	1898.2	4.5	63.6	32.0	0.0	0.0
64	2528.5	0.5	75.7	23.6	0.2	0.0
128	1152.8	-0.2	76.1	9.3	14.8	0.0
256	970.0	5.3	55.1	25.0	14.5	0.0
512	339.4	4.9	29.9	50.7	7.3	7.2
1024	312.7	5.1	27.8	50.0	9.9	7.2
2048	299.1	4.5	30.3	45.0	13.0	7.2

Runtime behaviour
Size	MFlops /sec	% of cycles used for
Size	MFlops /sec	±	Base	Exec	Cache	DTB	Branch	R dep	Nops
32	354.8	2.2	116.3	68.8	12.7	8.2	5.3	12.8	6.3
64	453.9	-0.3	136.8	107.8	1.9	21.5	0.1	0.0	5.8
128	205.5	-0.1	104.6	45.9	6.6	49.7	0.0	0.0	2.5
256	182.9	-0.1	108.4	34.6	65.7	4.6	0.0	0.0	3.6
512	63.7	0.0	102.3	11.6	87.2	2.3	0.0	0.0	1.2
1024	58.8	0.1	102.0	10.8	87.6	2.4	0.0	0.0	1.1
2048	55.9	-0.1	101.5	10.3	87.8	2.4	0.0	0.0	1.1

Table explanation

cs10-dime@fau.de

Last Modified: 10 January 2008