Abstract: A computer-implemented method of estimating the physical state of a fluid reservoir with known physical characteristics and subject to specified boundary conditions is provided. The fluid reservoir is represented as a plurality of nodes arranged in N-dimensional space, where N>1, each node representing a discrete finite volume of the fluid reservoir and being associated with a set of physical properties, the physical properties associated with the nodes together forming a vector x when arranged in order, with the vector x representing the physical state of the fluid reservoir, and where the discrete finite volumes together represent the entire fluid reservoir. The method includes for each of a plurality of iterations, estimating a change dx in the vector x that results in all relations being simultaneously satisfied, and at the end of each iteration updating the current value of x according to x=x+dx.

Abstract: Disclosed herein are methods, apparatuses, and techniques for estimating the state of a system. According to one implementation, a Massively Parallel Nested Factorisation technique, or MPNF, is disclosed that runs efficiently on parallel computer architectures. Also disclosed is a procedure used to create and utilize MPNF ordering.