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
A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex...A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.展开更多
In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed met...In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed method could provide control volumes with arbitrarygeometry and preserve the second-order accuracy even if highly distorted grids are used. Althougharbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are moredesirable for the simplicity of implementation and applications to engineering problems. Thepressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized MinimumResidual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linearequations. Four test cases were studied for validating the proposed method. In using this method,grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism ofproblems. Turbulence models can be simply integrated and the method can be straightforwardlyextended to treat three-dimensional problems.展开更多
Despite efficient parallelism in the solution of physical parameterization in the Global/Regional Assimilation and Prediction System(GRAPES),the Helmholtz equation in the dynamic core,with the increase of resolution,c...Despite efficient parallelism in the solution of physical parameterization in the Global/Regional Assimilation and Prediction System(GRAPES),the Helmholtz equation in the dynamic core,with the increase of resolution,can hardly achieve sufficient parallelism in the solving process due to a large amount of communication and irregular access.In this paper,optimizing the Helmholtz equation solution for better performance and higher efficiency has been an urgent task.An optimization scheme for the parallel solution of the Helmholtz equation is proposed in this paper.Specifically,the geometrical multigrid optimization strategy is designed by taking advantage of the data anisotropy of grid points near the pole and the isotropy of those near memory equator in the Helmholtz equation,and the Incomplete LU(ILU)decomposition preconditioner is adopted to speed up the convergence of the improved Generalized Conjugate Residual(GCR),which effectively reduces the number of iterations and the computation time.The overall solving performance of the Helmholtz equation is improved by thread-level parallelism,vectorization,and reuse of data in the cache.The experimental results show that the proposed optimization scheme can effectively eliminate the bottleneck of the Helmholtz equation as regards the solving speed.Considering the test results on a 10-node two-way server,the solution of the Helmholtz equation,compared with the original serial version,is accelerated by 100,with one-third of iterations reduced.展开更多
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A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.
文摘In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed method could provide control volumes with arbitrarygeometry and preserve the second-order accuracy even if highly distorted grids are used. Althougharbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are moredesirable for the simplicity of implementation and applications to engineering problems. Thepressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized MinimumResidual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linearequations. Four test cases were studied for validating the proposed method. In using this method,grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism ofproblems. Turbulence models can be simply integrated and the method can be straightforwardlyextended to treat three-dimensional problems.
基金partially supported by the Open Project of State Key Laboratory of Plateau Ecology and Agricuture,Qinghai University(No.2020-ZZ-03)the Qinghai Province High-End Innovative Thousand Talents Program Leading Talents+1 种基金the National Natural Science Foundation of China(Nos.61762074 and 61962051)the National Natural Science Foundation of Qinghai Province(No.2019-ZJ-7034)。
文摘Despite efficient parallelism in the solution of physical parameterization in the Global/Regional Assimilation and Prediction System(GRAPES),the Helmholtz equation in the dynamic core,with the increase of resolution,can hardly achieve sufficient parallelism in the solving process due to a large amount of communication and irregular access.In this paper,optimizing the Helmholtz equation solution for better performance and higher efficiency has been an urgent task.An optimization scheme for the parallel solution of the Helmholtz equation is proposed in this paper.Specifically,the geometrical multigrid optimization strategy is designed by taking advantage of the data anisotropy of grid points near the pole and the isotropy of those near memory equator in the Helmholtz equation,and the Incomplete LU(ILU)decomposition preconditioner is adopted to speed up the convergence of the improved Generalized Conjugate Residual(GCR),which effectively reduces the number of iterations and the computation time.The overall solving performance of the Helmholtz equation is improved by thread-level parallelism,vectorization,and reuse of data in the cache.The experimental results show that the proposed optimization scheme can effectively eliminate the bottleneck of the Helmholtz equation as regards the solving speed.Considering the test results on a 10-node two-way server,the solution of the Helmholtz equation,compared with the original serial version,is accelerated by 100,with one-third of iterations reduced.
