Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified...Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H-m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo-Elimination method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are further presented.展开更多
The underwater acoustic field influenced by a selected ocean internal wavewas computed using the Parabolic Equation (PE) method and split-step difference algorithm in thispaper. Acoustic field is formed by sound sourc...The underwater acoustic field influenced by a selected ocean internal wavewas computed using the Parabolic Equation (PE) method and split-step difference algorithm in thispaper. Acoustic field is formed by sound source with different frequency covering the range ofradiation noise of ships and submarines. Owing to the adoption of complex variables, sparse matrix,Gaussian source and analysis on the grid size, numerical results are achieved smoothly. The resultsshow that internal wave''s influence on underwater sound can''t be neglected, especially for highersound frequency. So it'' s necessary to take internal wave into account in identifying radiationnoise of ships and submarines, namely for sound intensity, transmission loss and spectra shape.展开更多
文摘Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H-m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo-Elimination method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are further presented.
文摘The underwater acoustic field influenced by a selected ocean internal wavewas computed using the Parabolic Equation (PE) method and split-step difference algorithm in thispaper. Acoustic field is formed by sound source with different frequency covering the range ofradiation noise of ships and submarines. Owing to the adoption of complex variables, sparse matrix,Gaussian source and analysis on the grid size, numerical results are achieved smoothly. The resultsshow that internal wave''s influence on underwater sound can''t be neglected, especially for highersound frequency. So it'' s necessary to take internal wave into account in identifying radiationnoise of ships and submarines, namely for sound intensity, transmission loss and spectra shape.
