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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
± 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
± 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
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