Fast Iterative Method for Processing Hamilton-Jacobi Equations

Abstract

A system and method are provided for a parallel processing of the Hamilton-Jacobi equation. A numerical method is provided to solve the Hamilton-Jacobi equation that can be used with various parallel architectures and an improved Godunov Hamiltonian computation.

1 . A method for analyzing the connected quality of a hydrocarbon reservoir, comprising:
 obtaining a model of a portion of the reservoir and dividing it into cells, each cell having a volume and attributes;   assigning a speed function to a portion of the cells;   choosing a reference cell;   determining a connectivity between cells in the reservoir using a solution to an Eikonal equation, describing a propagating front in a heterogeneous medium, said front progressing outward from a reference cell until an ending condition is met, the Eikonal equation being solved by a fast iteration method with propagation velocity as a function of spatial position being provided by the speed function; and   characterizing regions of the reservoir by their connective quality to the reference cell using the connectivity.   
     
     
         2 . A method as in  claim 1 , wherein step of choosing a reference cell comprises choosing multiple reference cells at different locations from each other in the reservoir. 
     
     
         3 . A method as in  claim 1 , further comprising: performing the steps of determining a connectivity and characterizing regions with respect for each reference cell chosen. 
     
     
         4 . A method as in  claim 1 , further comprising individually summing the connectivities for each cell in the reservoir with respect the reference cell. 
     
     
         5 . A method as in  claim 1 , wherein determining the connectivity between cells in the reservoir by solving an Eikonal equation further comprising:
 creating an active list of data point nodes in a grid that are capable of being computed in parallel;   computing solutions to the Hamilton-Jacobi equation for data point nodes in the grid in parallel using the active list of computing nodes;   expanding the active list of computing nodes during each computation iteration to include all data point nodes that are influenced by a current computation iteration;   updating the solutions on the data point nodes in the active list until the data point nodes converge; and   displaying the approximated solution using a display volume to an end user.