Patent Document ID: 9396162
Application ID: 13189149
Patent Flag: 1

Claim One:
1. A hardware implemented method comprising: estimating a physical state of a fluid reservoir with known physical characteristics, the estimating including creating an ordering of grid blocks for a parallel processing preconditioner, the creating including causing a processor to carry out the steps of: reading data describing one or more models of the fluid reservoir; defining a mesh of grid blocks based on the data, that represents a problem domain to be solved by an iterative method which uses the parallel processing preconditioner; determining a dominant direction for the mesh of grid blocks; defining a plurality of kernels having a color-based, non-planar organization, each kernel comprising matrix elements having connections within one or more adjacent lines of the grid blocks oriented along the dominant direction, including: determining how many lines are included in each kernel and how the lines are arranged within each kernel; determining at least two colors as color designations, wherein increasing a number of lines in a kernel or increasing a number of colors used produces a more accurate preconditioner and decreases a number of kernels that can be executed simultaneously; and assigning one of the color designations to each kernel, wherein an assembly of kernels of a given color forms a non-contiguous, non-planar structure and no adjacent kernels have a same color, except kernels adjacent to kernels of each available color; defining an order of processing by: defining an ordering from a first color to a last color; defining an ordering for the processing of each kernel within each color, including processing kernels of a given color in parallel; defining an ordering of grid blocks within each kernel along the dominant direction from one end of the kernel to another end of the kernel; adding one or more values from each corresponding grid block to a mathematical matrix in the defined order; generating the preconditioner based on the adding of one or more values from the grid blocks, the preconditioner comprising a mathematical preconditioning matrix that approximates an actual mathematical matrix and includes terms that are ordered by reference to the color assigned to each kernel and component grid blocks of each kernel; and predicting a current and/or a future physical state of the fluid reservoir based on processing the mathematical preconditioning matrix while maintaining a non-planar spatial organization of the kernels.