The NAS-BT code (sometimes referred to as APPBT or NPB-BT) is one of the NAS Parallel Benchmarks (NPB). The code uses an implicit algorithm to compute a finite difference solution to the 3D compressible Navier-Stokes equations. The solution is based on a Beam-Warming approximate factorisation. The approximate factorisation decouples the three dimensions. This leads to three sets of regularly structured systems of linear equations. The resulting equations are block tridiagonal which are solved using the Thomas algorithm (Gaussian elimination) without pivoting of a banded system. 

Code information: 4500 lines of source and 18 subroutines

Total Parallelization Time using ParaWise : Approximately 40 minutes.

User Time: Approximately 10 minutes.

  Results

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SGI Origin 2000

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Cray T3D

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Transtech Paramid

  SGI Origin 2000

 

ParaWise NPB2.3

1-D Partition

 ParaWise NPB2.3

2-D Partition

 NASA Manual NPB2.2

2-D Partition
Processors Speed Up Processors Speed Up Processors Speed Up
4 3.24 4(2x2) 3.37 4(2x2) 3.35
9 5.99 9(3x3) 6.80 9(3x3) 7.27
16 11.61 16(4x4) 11.63 16(4x4) 12.82
25 14.94 25(5x5) 19.18 25(5x5) 25.95
    49(7x7) 19.62 49(7x7) 34.13
    64(8x8) 34.32 64(8x8) 22.64

Results for NAS-BT (Ver. NPB2.3) on a 64x64x64 (Class A) grid on the SGI Origin for ParaWise one-dimensional and two-dimensional partitioning, and NASA manual two-dimensional parallelization (NPB2.2).

  Cray T3D

ParaWise NPB4.3

2-D Partition (64x64x64)
Processors Time(secs) Speed Up

1

13039*

-
32(4x8) 415.8 31.4
64(8x8) 213.3 61.1
128(8x16) 114.0 114.4
256(16x16) 60.6 215.1

* lower bound estimate for serial time (i.e. speed up is also lower bound)

Transtech Paramid

1-D Partition (32x32x32)

Processors

Synchronous Speed Up

Overlapping calc and comm

Speed Up
1 - -
2 1.64 1.76
4 2.39 3.06
8 3.35 4.99
12 3.75 5.96
16 4.24 7.31