Abstract: A system and method for preconditioning or smoothing (e.g., multi-color DILU preconditioning) for iterative solving of a system of equations. The method includes accessing a matrix comprising a plurality of coefficients of a system of equations and accessing coloring information corresponding to the matrix. The method further includes determining a diagonal matrix based on the matrix and the coloring information corresponding to the matrix. The determining of the diagonal matrix may be determined in parallel on a per color basis. The method may further include determining an updated solution to the system of equations where the updated solution is determined in parallel on a per color basis using the diagonal matrix.

Abstract: A preconditioner processor and a method of computing a preconditioning matrix. In one embodiment, the preconditioner processor has parallel computing pipelines including: (1) a graph coloring circuit operable to identify parallelisms in a sparse linear system, (2) an incomplete lower triangle, upper triangle factorization (ILU) computer configured to employ the parallel computing pipelines according to the parallelisms to: (2a) determine a sparsity pattern for an ILU preconditioning matrix, and (2b) compute non-zero elements of the ILU preconditioning matrix according to the sparsity pattern, and (3) a memory communicably couplable to the parallel computing pipelines and configured to store the ILU preconditioning matrix.

Abstract: A system, method, and computer program product are provided for performing graph aggregation. In use, a graph with a plurality of vertices and a plurality of edges is identified. Additionally, aggregation is performed on the vertices and edges of the graph by computing a graph matching, where such graph matching is performed in a data-parallel manner.

Abstract: A system, method, and computer program product are provided for performing graph aggregation. In use, a graph with a plurality of vertices and a plurality of edges is identified. Additionally, graph matching is performed on the vertices and edges of the graph by computing a graph matching, wherein the performance of the graph matching is optimized.

Abstract: A parallel multicolor ILU factorization preconditioner processor and a method of computing an ILU preconditioning matrix. One embodiment of the preconditioning processor having parallel computing pipelines includes: (1) a graph coloring circuit operable to identify parallelisms in a sparse linear system, (2) an ILU computer configured to employ the parallel computing pipelines according to the parallelisms to: (2a) determine a sparsity pattern for an ILU preconditioning matrix, and (2b) compute non-zero elements of the ILU preconditioning matrix according to the sparsity pattern, and (3) a memory communicably couplable to the parallel computing pipelines and configured to store the ILU preconditioning matrix.

Abstract: A system and method for preconditioning or smoothing (e.g., multi-color DILU preconditioning) for iterative solving of a system of equations. The method includes accessing a matrix comprising a plurality of coefficients of a system of equations and accessing coloring information corresponding to the matrix. The method further includes determining a diagonal matrix based on the matrix and the coloring information corresponding to the matrix. The determining of the diagonal matrix may be determined in parallel on a per color basis. The method may further include determining an updated solution to the system of equations where the updated solution is determined in parallel on a per color basis using the diagonal matrix.

Abstract: A system, method, and computer program product are provided for performing graph aggregation. In use, a graph with a plurality of vertices and a plurality of edges is identified. Additionally, graph matching is performed on the vertices and edges of the graph by computing a graph matching, wherein the performance of the graph matching is optimized.

Abstract: A system, method, and computer program product are provided for performing graph aggregation. In use, a graph with a plurality of vertices and a plurality of edges is identified. Additionally, aggregation is performed on the vertices and edges of the graph by computing a graph matching, where such graph matching is performed in a data-parallel manner.