We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about...We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.展开更多
A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special tec...A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.展开更多
A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient meth...A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.展开更多
The grid equations in decomposed domain by parallel computation are soled, and a method of local orthogonalization to solve the large-scaled numerical computation is presented. It constructs preconditioned iteration m...The grid equations in decomposed domain by parallel computation are soled, and a method of local orthogonalization to solve the large-scaled numerical computation is presented. It constructs preconditioned iteration matrix by the combination of predigesting LU decomposition and local orthogonalization, and the convergence of solution is proved. Indicated from the example, this algorithm can increase the rate of computation efficiently and it is quite stable.展开更多
In this paper two parallel algorithms for solving dense linear equations arediscussed. The algorithms are based on LU-decomposition followed by forward andbackward substitutions. The algorithms are numerically stable ...In this paper two parallel algorithms for solving dense linear equations arediscussed. The algorithms are based on LU-decomposition followed by forward andbackward substitutions. The algorithms are numerically stable and have been testedon the Sequent Balance Machine with efficient utilization of all processors.展开更多
A novel FEM called interface finite element method(I-FEM)is proposed for the step size-varying electro-quasistatic field(EQS)in this paper.First,the corresponding equation and interface conditions for I-FEM are given....A novel FEM called interface finite element method(I-FEM)is proposed for the step size-varying electro-quasistatic field(EQS)in this paper.First,the corresponding equation and interface conditions for I-FEM are given.Then,the numerical principle of I-FEM is conducted.In the proposed method,by the inverse matrix modification lemma,the calculation amount of I-FEM is decreased greatly.Furthermore,the corresponding example is given to verify the effectiveness and correctness of IFEM.At last,the error analysis and universal promotion of the proposed I-FEM are given.Compared with the normal FEM,I-FEM can greatly decrease the calculation amount while the numerical accuracy of I-FEM is even better than the normal FEM in some case.展开更多
This study presents the numerical results for the three dimensional natural gas air mixing in a rectangular subsonic channel under the standard datum state. The lower and upper decomposition method was employed to o...This study presents the numerical results for the three dimensional natural gas air mixing in a rectangular subsonic channel under the standard datum state. The lower and upper decomposition method was employed to obtain the solutions of the full Navier Stokes equations capable of describing compressible fluid mixing. Grid was generated by the area orthogonal technique. The results indicate that three dimensional mixing between Natural Gas (NG) and air has more complicated compressible waves around the injection nozzle. The presence of injection with large speed can suppress the boundary separation happened occurring at the top wall due to the channel expansion, but makes the near wake flow more complicated. The mixing region can be widened by increasing the injection speed. The recurrence of the vortex structure and the coherent structure can be found from the full Navier Stokes simulation. It can be concluded that the increase in the injection velocity can improve the effectiveness of mixing of NG and air in the near wake of the injectors.展开更多
基金supported by the National Basic Research Program(No.2005CB321702)the China Outstanding Young Scientist F0undation(No.10525102)the National Natural Science Foundation (No.10471146),P.R.China
文摘We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.
文摘A new favorable iterative algorithm named as PBiCGSTAB （preconditioned bi-conjugate gradient stabilized） algorithm is presented for solving large sparse complex systems. Based on the orthogonal list, the special technique of only storing non-zero elements is carried out. The incomplete LU factorization without fill-ins is adopted to reduce the condition number of the coefficient matrix. The BiCGSTAB algorithm is extended from the real system to the complex system and it is used to solve the preconditioned complex linear equations. The locked-rotor state of a single-sided linear induction machine is simulated by the software programmed with the finite element method and the PBiCGSTAB algorithm. Then the results are compared with those from the commercial software ANSYS, showing the validation of the proposed software. The iterative steps required for the proposed algorithm are reduced to about one-third, when compared to the BiCG method, therefore the algorithm is fast.
文摘A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.
文摘The grid equations in decomposed domain by parallel computation are soled, and a method of local orthogonalization to solve the large-scaled numerical computation is presented. It constructs preconditioned iteration matrix by the combination of predigesting LU decomposition and local orthogonalization, and the convergence of solution is proved. Indicated from the example, this algorithm can increase the rate of computation efficiently and it is quite stable.
文摘In this paper two parallel algorithms for solving dense linear equations arediscussed. The algorithms are based on LU-decomposition followed by forward andbackward substitutions. The algorithms are numerically stable and have been testedon the Sequent Balance Machine with efficient utilization of all processors.
基金supported by National Natural Science Foundation of China under Grant No.52077073.
文摘A novel FEM called interface finite element method(I-FEM)is proposed for the step size-varying electro-quasistatic field(EQS)in this paper.First,the corresponding equation and interface conditions for I-FEM are given.Then,the numerical principle of I-FEM is conducted.In the proposed method,by the inverse matrix modification lemma,the calculation amount of I-FEM is decreased greatly.Furthermore,the corresponding example is given to verify the effectiveness and correctness of IFEM.At last,the error analysis and universal promotion of the proposed I-FEM are given.Compared with the normal FEM,I-FEM can greatly decrease the calculation amount while the numerical accuracy of I-FEM is even better than the normal FEM in some case.
文摘This study presents the numerical results for the three dimensional natural gas air mixing in a rectangular subsonic channel under the standard datum state. The lower and upper decomposition method was employed to obtain the solutions of the full Navier Stokes equations capable of describing compressible fluid mixing. Grid was generated by the area orthogonal technique. The results indicate that three dimensional mixing between Natural Gas (NG) and air has more complicated compressible waves around the injection nozzle. The presence of injection with large speed can suppress the boundary separation happened occurring at the top wall due to the channel expansion, but makes the near wake flow more complicated. The mixing region can be widened by increasing the injection speed. The recurrence of the vortex structure and the coherent structure can be found from the full Navier Stokes simulation. It can be concluded that the increase in the injection velocity can improve the effectiveness of mixing of NG and air in the near wake of the injectors.
