System and method for multi-color dilu preconditioner
First Claim
1. A non-transitory computer-readable storage medium embodying instructions that, when executed by a processing device, cause the processing device to perform a method for preconditioning, said method comprising:
- accessing a matrix comprising a plurality of coefficients of a system of linear equations;
accessing coloring information corresponding to said matrix; and
determining a diagonal matrix of a preconditioning matrix of said matrix based on said matrix and said coloring information corresponding to said matrix, wherein said determining comprises;
assigning a plurality of execution threads to a plurality of elements of a respective color in said diagonal matrix; and
computing said plurality of elements of said respective color by executing said plurality of execution threads in said processing device.
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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.
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Citations
19 Claims
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1. A non-transitory computer-readable storage medium embodying instructions that, when executed by a processing device, cause the processing device to perform a method for preconditioning, said method comprising:
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accessing a matrix comprising a plurality of coefficients of a system of linear equations; accessing coloring information corresponding to said matrix; and determining a diagonal matrix of a preconditioning matrix of said matrix based on said matrix and said coloring information corresponding to said matrix, wherein said determining comprises; assigning a plurality of execution threads to a plurality of elements of a respective color in said diagonal matrix; and computing said plurality of elements of said respective color by executing said plurality of execution threads in said processing device. - View Dependent Claims (2, 3, 4, 5)
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6. The non-transitory computer-readable storage medium as described in claim herein said processing device comprises a graphics processing unit (GPU).
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7. A system for preconditioning, said system comprising:
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a processor; and memory coupled to said processor and comprising instructions that comprise; a matrix access module operable to access a matrix corresponding to a system of equations; a coloring access module operable to access color information corresponding to said matrix; and a diagonal matrix determination module operable for determining a diagonal matrix based on said color information corresponding to said matrix, wherein said determining comprises; assigning a plurality of execution threads to a plurality of elements of a respective color in said diagonal matrix; and computing said plurality of elements of said respective color by executing said plurality of execution threads in parallel in said processing device, wherein said diagonal matrix determination module is operable for computing an incomplete lower and upper triangular decomposition with only diagonal modified (DILU) preconditioner matrix. - View Dependent Claims (8, 9, 10, 11, 12, 13)
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14. A non-transitory computer-readable storage medium embodying instructions that, when executed by a processing device, cause the processing device to perform a method for solving a system of equations, said method comprising:
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accessing a matrix comprising coefficients of a system of equations; accessing coloring information corresponding to said matrix, wherein each row of said matrix is assigned with a particular color; determining a diagonal matrix of a preconditioning matrix of said matrix, wherein said determining said diagonal matrix comprises; assigning a plurality of execution threads to a plurality of elements of a respective color in said diagonal matrix; and computing said plurality of elements of said respective color by executing said plurality of execution threads in parallel in said processing device; and determining an updated solution to said system of equations, wherein said determining said updated solution is based on an incomplete lower and upper triangular decomposition with only diagonal modified (DILU) preconditioner performed by a graphics processing unit (GPU) and said updated solution is computed in parallel on a per color basis. - View Dependent Claims (15, 16, 17, 18, 19)
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Specification