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
We have optimized the parallel threshold ILU algorithm(ParILUT)for GPUs.The optimizations are for three building blocks:candidate search and ILU residual computation,adding and removing elements,and threshold selectio...We have optimized the parallel threshold ILU algorithm(ParILUT)for GPUs.The optimizations are for three building blocks:candidate search and ILU residual computation,adding and removing elements,and threshold selection.Firstly,we fuse candidate search and ILU residual computation by modifying the ParILUT algorithm and extending the register-aware SpGEMM algorithm to calculate it.At the same time,we developed a GPU bin search algorithm to make the register-aware SpGEMM algorithm perform better in ParILUT.Secondly,we adopt a warp-row-parallel approach to add elements to new L and U and remove elements from candidates instead of the thread-row-parallel approach.And used the efficient GPU instructions to locate the positions of elements.Thirdly,we proposed a balanced classification tree in the threshold selection to balance the buckets’data,when a large number of elements with the same value.Finally,we experimented with the performance of each optimization and the whole ParILUT.And verified the correctness of the optimized ParILUT.The result indicates that the optimized ParILUT average speedup is 4.03 times over the original version,and the speedup increases with the amount of fill-in.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supported by the National Natural Science Foundation of China,under Grant 62172389.
文摘We have optimized the parallel threshold ILU algorithm(ParILUT)for GPUs.The optimizations are for three building blocks:candidate search and ILU residual computation,adding and removing elements,and threshold selection.Firstly,we fuse candidate search and ILU residual computation by modifying the ParILUT algorithm and extending the register-aware SpGEMM algorithm to calculate it.At the same time,we developed a GPU bin search algorithm to make the register-aware SpGEMM algorithm perform better in ParILUT.Secondly,we adopt a warp-row-parallel approach to add elements to new L and U and remove elements from candidates instead of the thread-row-parallel approach.And used the efficient GPU instructions to locate the positions of elements.Thirdly,we proposed a balanced classification tree in the threshold selection to balance the buckets’data,when a large number of elements with the same value.Finally,we experimented with the performance of each optimization and the whole ParILUT.And verified the correctness of the optimized ParILUT.The result indicates that the optimized ParILUT average speedup is 4.03 times over the original version,and the speedup increases with the amount of fill-in.
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.
