Method For Solving Implicit Reservoir Simulation Matrix
First Claim
1. A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector, the method comprising:
- receiving the block sparse matrix and the right hand side block vector;
constructing a reduced transformed block sparse matrix from the block sparse matrix;
constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector;
wherein constructing the reduced transformed block sparse matrix comprises;
assembling one or more coefficients of one or more mass change terms from a column of the block sparse matrix into a column matrix;
performing a singular value decomposition on the column matrix to generate a left matrix, a diagonal matrix and a right matrix; and
discarding one or more singular values that are less than a predetermined threshold value to generate a reduced diagonal matrix; and
solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector.
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Abstract
A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector. In one embodiment, the method includes receiving the block sparse matrix and the right hand side block vector, constructing a reduced transformed block sparse matrix from the block sparse matrix, constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector, and solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector.
131 Citations
27 Claims
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1. A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector, the method comprising:
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receiving the block sparse matrix and the right hand side block vector;
constructing a reduced transformed block sparse matrix from the block sparse matrix;
constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector;
wherein constructing the reduced transformed block sparse matrix comprises;
assembling one or more coefficients of one or more mass change terms from a column of the block sparse matrix into a column matrix;
performing a singular value decomposition on the column matrix to generate a left matrix, a diagonal matrix and a right matrix; and
discarding one or more singular values that are less than a predetermined threshold value to generate a reduced diagonal matrix; and
solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22)
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23. A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector, the method comprising:
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constructing a reduced transformed block sparse matrix from the block sparse matrix;
constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector;
solving for a reduced transformed solution change block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector;
converting the reduced transformed solution change block vector to a solution change block vector having one or more changes in mass unknowns and one or more changes in pressure unknowns; and
adding the solution change block vector to a current estimate of the solution block vector to update the solution block vector.
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24. A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a first block vector and X represents a solution block vector, the method comprising:
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receiving the block sparse matrix and the first block vector;
constructing a reduced transformed block sparse matrix from the block sparse matrix;
constructing a reduced transformed residual block vector from the block sparse matrix and the first block vector;
wherein constructing the reduced transformed block sparse matrix comprises;
assembling at least one coefficient associated with the at least one mass change term from a column of the block sparse matrix into a column matrix;
performing a singular value decomposition on the column matrix to generate a first matrix, a second matrix and a third matrix; and
discarding each singular value less than a predetermined threshold value to generate a reduced diagonal matrix; and
solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector. - View Dependent Claims (25, 26, 27)
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Specification