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

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.

Abstract: A computer-implemented method is provided of estimating the physical state of a physical system with known physical characteristics and subject to specified boundary conditions. The system is represented as a plurality of nodes arranged in N-dimensional space, where N is an integer greater than 1, each node being associated with a set of physical properties, the physical properties associated with the nodes together forming a vector x when arranged in order, such that the vector x represents the physical state of the system. Physical data is received relating to the boundary conditions and the physical characteristics of the system, and it is determined from the received data the relations which must be satisfied by the component elements of the vector x, the number of relations being sufficient to determine the value of all elements of x. An initial estimate x0 is received or determined for the physical properties which will satisfy the relations.