Improved constrained pressure residual preconditioner for efficient solution of the adjoint equation

摘要

A method, system and computer program product is disclosed for using a constrained pressure residual (CPR) preconditioner to solve adjoint models. A linear system of fluid flow equations comprising a plurality of variables that represent fluid flow properties in a geological formation of a subterranean reservoir is provided. Matrix (Ã ) T , which comprises a transpose of a Jacobian matrix associated with the linear system of fluid flow equations, is constructed. A constrained pressure residual preconditioner is constructed responsive to the matrix (Ã ) T . Matrix equation (Ã ) T y = d is then solved using the constrained pressure residual preconditioner.