Patent ID: 7418370

Claim:
A method to determine information indicative of at least one property of a physical entity by utilizing a linear system of equations to represent the physical entity, the method comprising: generating a mesh representation of the physical entity, wherein the mesh representation comprises a plurality of mesh elements; computing a linear system matrix A of coefficients by computing interactions between simple functions defined over sets of mesh elements; partitioning the mesh representation into a plurality of partitions separated by partition boundaries, wherein each partition comprises at least one mesh element of the plurality of mesh elements, wherein at least one partition comprises at least two mesh elements of the plurality of mesh elements; computing, using at least the plurality of partitions, a preconditioner for the linear system matrix A, wherein the preconditioner is compatible with the linear system of equations and provides at least basis function support over at least two mesh elements, where coupling of the preconditioner between partitions is only through basis functions at the partition boundaries; using at least the linear system matrix A and the preconditioner, determining an approximate numerical solution of the linear system of equations, wherein the approximate numerical solution comprises the information indicative of at least one property of the physical entity, wherein the at least one property comprises a fluid mechanical property; and outputting the approximate numerical solution.