In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix spl...In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive definite.From the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions.Numerical examples demonstrate that the presented method precede to other methods in practical implementation.展开更多
For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matr...For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.展开更多
We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix...We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix.Theoretical analysis gives the choice of parameter matrix involved based on the H-compatible splitting of the sys-tem matrix.Moreover,in actual implementation,the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied.Numeri-cal experiments show that the method is efficient and further verify the convergence theorems.展开更多
Based on the combination of Racah＇s group-theoretical consideration with Slater＇s wavefunction, a 91 ×91 complete energy matrix is established in tetragonal ligand field D2d for Pr3＋ ion. Thus, the Stark energ...Based on the combination of Racah＇s group-theoretical consideration with Slater＇s wavefunction, a 91 ×91 complete energy matrix is established in tetragonal ligand field D2d for Pr3＋ ion. Thus, the Stark energy-levels of Pr3＋ ions doped separately in LiYF4 and LiBiF4 crystals are calculated, and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions. Besides, the influence of Pr3＋ on energy-level splitting is investigated, and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities. We see that the energy splitting patterns are similar and the crystal field interaction of LiYF4：Pr3＋ is stronger than that of LiBiF4：Pr3＋.展开更多
Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtaine...Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.展开更多
In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a...In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.展开更多
Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the ...Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.展开更多
Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is...Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.展开更多
Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyc...Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.展开更多
To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corres...To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.展开更多
Adiabatic shear behavior and the corresponding mechanism of TiB2/Al composites were researched by split Hopkinson pressure bar （SHPB）.Results show that the flow stresses of the TiB2/Al composites exhibit softening t...Adiabatic shear behavior and the corresponding mechanism of TiB2/Al composites were researched by split Hopkinson pressure bar （SHPB）.Results show that the flow stresses of the TiB2/Al composites exhibit softening tendency with the increasing of strain rates. All the composites fail in splitting and cutting with a 45 degree, and the phase transformed bands of molten aluminum are found on the adiabatic shear layers. The deformation behavior and shear localization of the TiB2/Al composites specimens were simulated by finite element code MSC.Marc. The Johnson-Cook model was used to describe the thermo-viscoplastic response of the specimen material. There was unanimous between the numerical result and the experimental result on the location of the adiabatic shear band. From the numerical simulation and experiment, it was concluded that the instantaneous failure of the composite was ascribed due to the local low strength area where the formation of adiabatic shear band was, and the stress condition had significant effect on the initiation and propagation of adiabatic shear band （ASB）.展开更多
基金This work is supported by the National Natural Science Foundation of China with No.11461046the Natural Science Foundation of Jiangxi Province of China with Nos.20181ACB20001 and 20161ACB21005.
文摘In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive definite.From the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions.Numerical examples demonstrate that the presented method precede to other methods in practical implementation.
文摘For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.
基金This work was supported by the National Natural Science Foundation of China(No.11271289,11701221)the Fundamental Research Funds for the Central Universities.
文摘We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix.Theoretical analysis gives the choice of parameter matrix involved based on the H-compatible splitting of the sys-tem matrix.Moreover,in actual implementation,the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied.Numeri-cal experiments show that the method is efficient and further verify the convergence theorems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10774103 and 10974138)
文摘Based on the combination of Racah＇s group-theoretical consideration with Slater＇s wavefunction, a 91 ×91 complete energy matrix is established in tetragonal ligand field D2d for Pr3＋ ion. Thus, the Stark energy-levels of Pr3＋ ions doped separately in LiYF4 and LiBiF4 crystals are calculated, and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions. Besides, the influence of Pr3＋ on energy-level splitting is investigated, and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities. We see that the energy splitting patterns are similar and the crystal field interaction of LiYF4：Pr3＋ is stronger than that of LiBiF4：Pr3＋.
基金Supported by National Natural Science Foundation of China
文摘Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.
文摘In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.
基金supported by the National Natural Science Foundation of China(Grant No.12161030)by the Hainan Provincial Natural Science Foundation of China(Grant No.121RC537).
文摘Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.
文摘Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.
文摘Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.
文摘To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.
基金the National Engineering Research Center Open Fund(No.2011007B)Natural Science Foundation of GuangDong Province(No.10451064101004631)
文摘Adiabatic shear behavior and the corresponding mechanism of TiB2/Al composites were researched by split Hopkinson pressure bar （SHPB）.Results show that the flow stresses of the TiB2/Al composites exhibit softening tendency with the increasing of strain rates. All the composites fail in splitting and cutting with a 45 degree, and the phase transformed bands of molten aluminum are found on the adiabatic shear layers. The deformation behavior and shear localization of the TiB2/Al composites specimens were simulated by finite element code MSC.Marc. The Johnson-Cook model was used to describe the thermo-viscoplastic response of the specimen material. There was unanimous between the numerical result and the experimental result on the location of the adiabatic shear band. From the numerical simulation and experiment, it was concluded that the instantaneous failure of the composite was ascribed due to the local low strength area where the formation of adiabatic shear band was, and the stress condition had significant effect on the initiation and propagation of adiabatic shear band （ASB）.
