SAYLR3: Saylor's petroleum engineering/reservoir simulation matrices 3D reservior (10x10x10)
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From 3D simulation of reservoirs in which shale poses vertical barriers to fluid flow and creates an almost random heterogeneity in the coefficient matrix. There are, in addition, enormous local contrasts in the transmissibility coefficients of the differential equation. These properties characterize matrices that are difficult to solve. This matrix is almost identical to the matrix SHERMAN1 which is one of the oil reservoir simulation challenge matrices contributed by Andy Sherman of Nolan and Associates.

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Size
Type
1000 x 1000, 375 entries
real unsymmetric
Nonzeros
total diagonal below diagonal above diagonal A-A' 3750 1000 1375 1375 0

Column Data
Row Data
Average nonzeros per column : 3.8 Standard deviation : 2

index nonzeros longest 214 7 shortest 101 1

Average nonzeros per row : 3.8 Standard deviation : 2

index nonzeros longest 214 7 shortest 101 1

Bandwidths
Profile Storage
lower 101 upper 101 average |i-j| 20 std.dev. 36

min max ave. std.dev. lower bandwidth 1 101 36 44 upper bandwidth 1 101 36 44

Symmetric skyline storage requirement: 35740

Heaviest diagonals
offset from main 0 -10 10 -1 1 -100 100
nonzeros 1000 598 598 462 462 315 315
accumulated percent 26.67 42.61 58.56 70.88 83.20 91.60 100.00

Top 7 out of 7 nonvoid diagonals.
Conditioning
Frobenius norm 43 condition number (est.) 1e+02 2-norm (est.) 5 diagonal dominance no

Set Information
Set SAYLOR
Source:
Richard Kendall, Don Peaceman, Herb Stone, and Bill Watts, Exxon
Discipline: Oil reservoir modeling
Accession: Summer 1984

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