Bordered linear systems arise from many industrial applications, such as reservoir simulation and structural engineering. Traditional ILU preconditioners which throw away the additional equations are often too crude f...Bordered linear systems arise from many industrial applications, such as reservoir simulation and structural engineering. Traditional ILU preconditioners which throw away the additional equations are often too crude for these systems. We describe a practical implementation of ILU preconditioners which are more accurate and more robust. The emphasis of this paper is on implementation rather than on theory.展开更多
In this paper, the Relaxed-ILU preconditioner is applied to solve the linear equations arising from the black oil models. Numerical experiments demonstrate that the method is superior to the ILU preconditioner which i...In this paper, the Relaxed-ILU preconditioner is applied to solve the linear equations arising from the black oil models. Numerical experiments demonstrate that the method is superior to the ILU preconditioner which is already extensively used in reservoir simulations. We have implemented the relaxed-ILU preconditioner into some practical reservoir simulators.展开更多
Iterative ILU factorizations are constructed,analyzed and applied as preconditioners to solve both linear systems and eigenproblems.The computational kernels of these novel Iterative ILU factorizations are sparse matr...Iterative ILU factorizations are constructed,analyzed and applied as preconditioners to solve both linear systems and eigenproblems.The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications,which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes.We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations.The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.展开更多
文摘Bordered linear systems arise from many industrial applications, such as reservoir simulation and structural engineering. Traditional ILU preconditioners which throw away the additional equations are often too crude for these systems. We describe a practical implementation of ILU preconditioners which are more accurate and more robust. The emphasis of this paper is on implementation rather than on theory.
基金Project(42274083) supported by the National Natural Science Foundation of ChinaProject(2023JJ30659) supported by Hunan Provincial Natural Science Foundation of China。
文摘In this paper, the Relaxed-ILU preconditioner is applied to solve the linear equations arising from the black oil models. Numerical experiments demonstrate that the method is superior to the ILU preconditioner which is already extensively used in reservoir simulations. We have implemented the relaxed-ILU preconditioner into some practical reservoir simulators.
基金The authors are members of the INdAM Research group GNCS and their research is partially supported by IMATI/CNR,by PRIN/MIUR and the Dipartimenti di Eccellenza Program 2018-22-Dept,of Mathematics,University of Pavia.
文摘Iterative ILU factorizations are constructed,analyzed and applied as preconditioners to solve both linear systems and eigenproblems.The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications,which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes.We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations.The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.
