A system, comprising: a housing having sensors to be operated in a first well; and a number of processors communicatively coupled to the housing, the processors to receive formation and/or fluid property information from the sensors, and 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 (tnet) subdivisions of the network, and then for inter-well (xnet) subdivisions of the network, wherein the unknowns of each subdivision of the network are assignable to different processors, wherein the network equations comprise connection equations, perforation equations, and mass balance equations, and wherein the computing is based on default values of the unknowns, or prior determined values of the unknowns, along with the formation and/or fluid property information, construct a distributed Jacobian matrix having portions comprising coefficients of the unknowns distributed among the 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, and wherein each processor only needs to determine the coefficients of the unknowns local to that particular processor; at least partially factor, in parallel, the Jacobian matrix to provide factors and eliminate some of the unknowns including at least one of pressures at nodes, fluid compositions at nodes, or flow rates at connections; and back-solve, in parallel, for any remaining unsolved ones of the unknowns, using the factors. a housing having sensors to be operated in a first well; and a number of processors communicatively coupled to the housing, the processors to receive formation and/or fluid property information from the sensors, and 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 (tnet) subdivisions of the network, and then for inter-well (xnet) subdivisions of the network, wherein the unknowns of each subdivision of the network are assignable to different processors, wherein the network equations comprise connection equations, perforation equations, and mass balance equations, and wherein the computing is based on default values of the unknowns, or prior determined values of the unknowns, along with the formation and/or fluid property information, construct a distributed Jacobian matrix having portions comprising coefficients of the unknowns distributed among the 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, and wherein each processor only needs to determine the coefficients of the unknowns local to that particular processor; at least partially factor, in parallel, the Jacobian matrix to provide factors and eliminate some of the unknowns including at least one of pressures at nodes, fluid compositions at nodes, or flow rates at connections; and back-solve, in parallel, for any remaining unsolved ones of the unknowns, using the factors.