In some embodiments, systems, methods, and articles may operate to compute, in parallel, to determine values of unknowns in network equations associated with a network of sub-surface wells and at least one surface facility, for intra-well subdivisions of the network, and then for inter-well subdivisions of the network, wherein the computing is based on default values of the unknowns, or prior determined values of the unknowns. Additional activities may include constructing a distributed Jacobian matrix having portions comprising coefficients of the unknowns distributed among a number of processors, wherein each of the portions is distributed to a particular one of the processors previously assigned to corresponding ones of the subdivisions. The Jacobian matrix may be factored to provide factors and eliminate some of the unknowns. Back-solving is used to determine remaining unsolved ones of the unknowns, using the factors. Additional apparatus, systems, and methods are described.