In the summer of 1984, Andy Sherman of Nolan and Associates, Houston, TX, USA, issued a challenge to the petroleum industry and the numerical analysis community for the fastest solution to a set of 5 systems of linear equations extracted from oil reservoir modeling programs. These are those five matrices. Each matrix arises from a three dimensional simulation model on a NX × NY × NZ grid using a seven-point finite-difference approximation with NC equations and unknowns per grid block. The corresponding right-hand side vector is also supplied. Symmetric matrices from partial differential equations (PDEs)

Matrices in this set:

SHERMAN1 (real symmetric, 1000 by 1000, 3750 entries), Black oil simulation, shale barriers (NX = NY = NZ = 10, NC = 1 )

SHERMAN2 (real unsymmetric, 1080 by 1080, 23094 entries), Thermal simulation with steam injection (NX = NY = 6, NZ = 5, NC = 5 )

SHERMAN3 (real unsymmetric, 5005 by 5005, 20033 entries), IMPES simulation of a black oil model (NX = 35, NY = 11, NZ = 13, NC = 1 )

SHERMAN4 (real unsymmetric, 1104 by 1104, 3786 entries), IMPES simulation with flow barriers (NX = 16, NY = 23, NZ = 3, NC = 1 )

SHERMAN5 (real unsymmetric, 3312 by 3312, 20793 entries), Fully implicit black oil model (NX = 16, NY = 23, NZ = 3, NC = 3 )