Patent ID: 7933752

Claim:
A digital processing system operable 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 digital processing system comprising: a generator configured to output a mesh representation of the physical entity, the mesh representation comprises a plurality of mesh elements; a first computation function configured to compute a linear system matrix A of coefficients by computing interactions between simple functions defined over sets of mesh elements; a partitioner configured to partition 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; a second computation function configured to compute, 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; a solver configured to determine, using at least the linear system matrix A and the preconditioner, 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 an output configured to return the approximate numerical solution.