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Foil 6 Structure of Sparse Matrices in NAS Benchmarks

From Spatial Differencing and ADI Solution of the NAS Benchmarks CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox


Nonzero structure of typical row of RHS is:
with 5 nonzeros about diagonal and two bands -- each with two nonzeros -- each side of diagonal
Each corresponds to a 5 by 5 (number of CFD labels) block matrix which is approximately "full"
So each of 5 NNAS3 rows of RHS has 65 nonzero elements
This can be contrasted with simple differencing to solve three dimensional Laplace equation Ñ2Y=0 where nonzero structure of typical row is:
with 7 nonzeros in each row of row of underlying matrix
  • Extra complexity of CFD makes parallel algorithms have better performance as calculation/communication ratio increased



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