First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti...First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT : K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.展开更多
In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back proj...In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.展开更多
A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions a...A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.展开更多
The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
A hybrid method for synthesizing antenna's three dimensional (3D) pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone con...A hybrid method for synthesizing antenna's three dimensional (3D) pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone conformal phased arrays are projected to the tangent plane in one generatrix of the truncated cone. Then two dimensional (2D) Chebyshev amplitude distribution optimization is respectively used in two mutual vertical directions of the tangent plane. According to the location of the elements, the excitation current amplitude distribution of each element on the conformal structure is derived reversely, then the excitation current amplitude is further optimized by using the genetic algorithm (GA). A truncated cone problem with 8x8 elements on it, and a 3D pattern desired side lobe level (SLL) up to 35 dB, is studied. By using the hybrid method, the optimal goal is accomplished with acceptable CPU time, which indicates that this hybrid method for the low sidelobe synthesis is feasible.展开更多
For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the ...For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the super-data envelopment analysis(DEA) model and the gray system theory, a new super-DEA for measuring the weight is proposed, and a gray relation projection model is established to rank the equipment programs. Finally, this approach is used to evaluate the equipment program. The results are verified valid and can provide a new way for evaluating the equipment program.展开更多
A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v...A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.展开更多
We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted ...Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad...In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.展开更多
In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We the...In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.展开更多
In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient proje...In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.展开更多
Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczm...Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.展开更多
A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th...A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.展开更多
In this paper,we present some sufficient conditions for constructing the bases of the left and the right spaces to ensure the feasibility of the oblique projection method and the extended oblique projection method.
In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale...In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.展开更多
We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessar...We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well.展开更多
A new pressure Poisson equation method with viscous terms is established on staggered grids. The derivations show that the newly established pressure equation has the identical equation form in the projection method. ...A new pressure Poisson equation method with viscous terms is established on staggered grids. The derivations show that the newly established pressure equation has the identical equation form in the projection method. The results show that the two methods have the same velocity and pressure values except slight differences in the CPU time.展开更多
In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of th...In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.展开更多
文摘First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT : K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.
基金supported by the National Key R&D Program of China(No.2022YFF0800601)National Scientific Foundation of China(Nos.41930103 and 41774047).
文摘In this study,the vertical components of broadband teleseismic P wave data recorded by China Earthquake Network are used to image the rupture processes of the February 6th,2023 Turkish earthquake doublet via back projection analysis.Data in two frequency bands(0.5-2 Hz and 1-3 Hz)are used in the imaging processes.The results show that the rupture of the first event extends about 200 km to the northeast and about 150 km to the southwest,lasting~90 s in total.The southwestern rupture is triggered by the northeastern rupture,demonstrating a sequential bidirectional unilateral rupture pattern.The rupture of the second event extends approximately 80 km in both northeast and west directions,lasting~35 s in total and demonstrates a typical bilateral rupture feature.The cascading ruptures on both sides also reflect the occurrence of selective rupture behaviors on bifurcated faults.In addition,we observe super-shear ruptures on certain fault sections with relatively straight fault structures and sparse aftershocks.
基金Project (50975263) supported by the National Natural Science Foundation of ChinaProject (2010081015) supported by International Cooperation Project of Shanxi Province, China+1 种基金 Project (2010-78) supported by the Scholarship Council in Shanxi province, ChinaProject (2010420120005) supported by Doctoral Fund of Ministry of Education of China
文摘A new algorithm based on the projection method with the implicit finite difference technique was established to calculate the velocity fields and pressure.The calculation region can be divided into different regions according to Reynolds number.In the far-wall region,the thermal melt flow was calculated as Newtonian flow.In the near-wall region,the thermal melt flow was calculated as non-Newtonian flow.It was proved that the new algorithm based on the projection method with the implicit technique was correct through nonparametric statistics method and experiment.The simulation results show that the new algorithm based on the projection method with the implicit technique calculates more quickly than the solution algorithm-volume of fluid method using the explicit difference method.
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
基金supported by the Fundamental Research Funds for the Central Universities(YWF-13D2-XX-13)the National High-tech Research and Development Program(863 Program)(2008AA121802)
文摘A hybrid method for synthesizing antenna's three dimensional (3D) pattern is proposed to obtain the low sidelobe feature of truncated cone conformal phased arrays. In this method, the elements of truncated cone conformal phased arrays are projected to the tangent plane in one generatrix of the truncated cone. Then two dimensional (2D) Chebyshev amplitude distribution optimization is respectively used in two mutual vertical directions of the tangent plane. According to the location of the elements, the excitation current amplitude distribution of each element on the conformal structure is derived reversely, then the excitation current amplitude is further optimized by using the genetic algorithm (GA). A truncated cone problem with 8x8 elements on it, and a 3D pattern desired side lobe level (SLL) up to 35 dB, is studied. By using the hybrid method, the optimal goal is accomplished with acceptable CPU time, which indicates that this hybrid method for the low sidelobe synthesis is feasible.
基金supported by the National Natural Science Foundation of China(7107307971222106+2 种基金70901069)the Research Foundation of the National Excellent Doctoral Dissertation of Chinathe Research Fund for the Doctoral Program of Higher Education(20133402110028)
文摘For the gray attributes of the equipment program and its difficulty to carry out the quantitative assessment of the equipment program information, the gray relation projection method is simply reviewed. Combining the super-data envelopment analysis(DEA) model and the gray system theory, a new super-DEA for measuring the weight is proposed, and a gray relation projection model is established to rank the equipment programs. Finally, this approach is used to evaluate the equipment program. The results are verified valid and can provide a new way for evaluating the equipment program.
基金supported by the National Natural Science Foundation of China (Nos. 10971203 and 11271340)the Research Fund for the Doctoral Program of Higher Education of China (No. 20094101110006)
文摘A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
基金Supported by the National Natural Science Foundation of China (No. 202001036)
文摘We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
基金Project supported by the National Natural Science Foundation of China (No.50278046)
文摘Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
基金Supported by National Natural Science Foundation of China (No.51275348)College Students Innovation and Entrepreneurship Training Program of Tianjin University (No.201210056339)
文摘In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000.
基金The project supported by the China NKBRSF(2001CB409604)
文摘In this paper, a fully third-order accurate projection method for solving the incompressible Navier-Stokes equations is proposed. To construct the scheme, a continuous projection procedure is firstly presented. We then derive a sufficient condition for the continuous projection equations to be temporally third-order accurate approximations of the original Navier-Stokes equations by means of the localtruncation-error-analysis technique. The continuous projection equations are discretized temporally and spatially to third-order accuracy on the staggered grids, resulting in a fully third-order discrete projection scheme. The possibility to design higher-order projection methods is thus demonstrated in the present paper. A heuristic stability analysis is performed on this projection method showing the probability of its being stable. The stability of the present scheme is further verified through numerical tests. The third-order accuracy of the present projection method is validated by several numerical test cases.
文摘In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.
文摘Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.
基金This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada(Grant OGPIN-336)and by the"Ministere de l'Education du Quebec"(FCAR Grant-ER-0725)
文摘A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.
基金Supported by The National Natural Science Foundation of China
文摘In this paper,we present some sufficient conditions for constructing the bases of the left and the right spaces to ensure the feasibility of the oblique projection method and the extended oblique projection method.
基金The subject is supported by Natural Science Foundation of China and Natural Science Foundation of Shandong Province.
文摘In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.
基金Supported by the National Natural Science Foundation of China
文摘We extend the oblique projection method given by Y.Saad to solve the generalized least squares problem. The corresponding oblique projection operator is presented and the convergence theorems are proved. Some necessary and sufficient conditions for computing the solution or the minimum N-norm solution of the min || A x- b ||M2 have been proposed as well.
基金Project supported by the National Natural Science Foundation of China (No. 50876114)
文摘A new pressure Poisson equation method with viscous terms is established on staggered grids. The derivations show that the newly established pressure equation has the identical equation form in the projection method. The results show that the two methods have the same velocity and pressure values except slight differences in the CPU time.
基金supported by National Natural Science Foundation of China (No. 10771120)Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.