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High-precision downward continuation of potential fi elds algorithm utilizing adaptive damping coeffi cient of generalized minimal residuals 被引量:1
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作者 Zhang Zhi-Hou Liao Xiao-Long +6 位作者 Shi Ze-Yu Lowry Anthony R. Yao Yu Lu Run-Qi Fan Xiang-Tai Liu Peng-Fei Zhao Si-Wei 《Applied Geophysics》 SCIE CSCD 2020年第5期672-686,900,共16页
The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration b... The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane.This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications.However,the downward continuation of potential fields is a typical linear inverse problem that is ill-posed.Generalized minimal residuals(GMRES)is an eff ective solution to ill-posed inverse problems,but it is unstable under the condition wherein the GMRES is directly applied in the calculation process.Moreover,the long-term behavior of its iterative computation is a disordered,divergent result.Therefore,to obtain stable solutions,GMRES is applied to solve the normal equations of the downward continuation of potential fields;it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient,thus strengthening the stability conditions of the equations of residual minimization.Finally,the stable downward continuation of the potential fields method is proposed.As indicated by the theoretical data and the measured testing data,the method proposed in this paper has the advantages of high-precision and excellent stability.Furthermore,compared with the Tikhonov iteration method,the proposed method avoids the need to choose regularization parameters. 展开更多
关键词 Potential fi elds generalized minimal residual method high precision and stable downward continuation
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Two-Parameter Block Triangular Splitting Preconditioner for Block Two-by-Two Linear Systems
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作者 Bo Wu Xingbao Gao 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1601-1615,共15页
This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster aroun... This paper proposes a two-parameter block triangular splitting(TPTS)preconditioner for the general block two-by-two linear systems.The eigenvalues of the corresponding preconditioned matrix are proved to cluster around 0 or 1 under mild conditions.The limited numerical results show that the TPTS preconditioner is more efficient than the classic block-diagonal and block-triangular preconditioners when applied to the flexible generalized minimal residual(FGMRES)method. 展开更多
关键词 Block triangular splitting Block two-by-two linear systems Eigenvalues PRECONDITIONER flexible generalized minimal residual(FGMRES)
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Fault detection and optimization for networked control systems with uncertain time-varying delay 被引量:2
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作者 Qing Wang Zhaolei Wang +1 位作者 Chaoyang Dong Erzhuo Niu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第3期544-556,共13页
The observer-based robust fault detection filter design and optimization for networked control systems (NOSs) with uncer- tain time-varying delays are addressed. The NCSs with uncertain time-varying delays are model... The observer-based robust fault detection filter design and optimization for networked control systems (NOSs) with uncer- tain time-varying delays are addressed. The NCSs with uncertain time-varying delays are modeled as parameter-uncertain systems by the matrix theory. Based on the model, an observer-based residual generator is constructed and the sufficient condition for the existence of the desired fault detection filter is derived in terms of the linear matrix inequality. Furthermore, a time domain opti- mization approach is proposed to improve the performance of the fault detection system. To prevent the false alarms, a new thresh- old function is established, and the solution of the optimization problem is given by using the singular value decomposition (SVD) of the matrix. A numerical example is provided to illustrate the effectiveness of the proposed approach. 展开更多
关键词 fault detection networked control systems residual generator time-varying delay time domain optimization approach.
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Unified control and detection framework and its applications: a review, some new results, and future perspectives 被引量:1
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作者 DING Steven Xianchuan LI Linlin JIANG Bin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2021年第5期995-1013,共19页
Initiated three decades ago,integrated design of controllers and fault detectors has continuously attracted research attention.The recent development of the unified control and detection framework with an observer-bas... Initiated three decades ago,integrated design of controllers and fault detectors has continuously attracted research attention.The recent development of the unified control and detection framework with an observer-based residual generator in its core gives a more general form of the previous works.Its applications to residual centred modelling of uncertain control systems,fault detection in feedback control systems with uncertainties,fault-tolerant control(FTC)as well as control performance degradation monitoring,detection and recovery are introduced.In conclusion,some future perspectives are proposed. 展开更多
关键词 unified framework of control and detection observer-based residual generator Youla parameterisation detection of additive and multiplicative faults in control loop fault-tolerant control(FTC) loop performance degradation(LPD)monitoring and recovery
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Observer-based fault detection scheme for a class of discrete time-delay systems
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作者 钟麦英 张承慧 +1 位作者 Ding Steven X Lain James 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2004年第3期288-294,共7页
In this contribution, robust fault detection problems for discrete time-delay systems with l2-norm bounded unknown inputs are studied. The basic idea of our study is first to introduce a state-memoryless observer-base... In this contribution, robust fault detection problems for discrete time-delay systems with l2-norm bounded unknown inputs are studied. The basic idea of our study is first to introduce a state-memoryless observer-based fault detection filter (FDF) as the residual generator and then to formulate such a FDF design problem as an Hen optimization problem in the sense of increasing the sensitivity of residual to the faults, while simultaneously enhancing the robustness of residual to unknown input as well as plant input. The main results consist of the formulation of such a residual generation optimization problem, solvability conditions and the derivation of an analytic solution. The residual evaluation problem is also considered, which includes the determination of residual evaluation function and threshold. A numerical example is used to demonstrate the proposed fault detection scheme. 展开更多
关键词 residual generator ROBUSTNESS unknown input time-delay system post-filter.
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A Model-free Approach to Fault Detection of Continuous-time Systems Based on Time Domain Data
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作者 Steven X. Ding 《International Journal of Automation and computing》 EI 2007年第2期189-194,共6页
In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to d... In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to directly identify parameters of the observer-based residual generator based on a numerically reliable data equation obtained by filtering and sampling the input and output signals. 展开更多
关键词 Fault detection linear continuous time-invariant systems time domain data subspace methods observer-based residual generator
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Application of A Fast Multipole BIEM for Flow Diffraction from A 3D Body 被引量:4
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作者 滕斌 宁德志 《海洋工程:英文版》 EI 2004年第2期291-298,共8页
A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to... A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers. 展开更多
关键词 fast multipole method boundary integral equation method generalized conjugate residual method current diffraction
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Fully coupled flow-induced vibration of structures under small deformation with GMRES method 被引量:2
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作者 张立翔 郭亚昆 张洪明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第1期87-96,共10页
Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompress... Lagrangian-Eulerian formulations based on a generalized variational principle of fluid-solid coupling dynamics are established to describe flow-induced vibration of a structure under small deformation in an incompressible viscous fluid flow. The spatial discretization of the formulations is based on the multi-linear interpolating functions by using the finite element method for both the fluid and solid structures. The generalized trapezoidal rule is used to obtain apparently non-symmetric linear equations in an incremental form for the variables of the flow and vibration. The nonlinear convective term and time factors are contained in the non-symmetric coefficient matrix of the equations. The generalized minimum residual (GMRES) method is used to solve the incremental equations. A new stable algorithm of GMRES-Hughes-Newmark is developed to deal with the flow-induced vibration with dynamical fluid-structure interaction in complex geometries. Good agreement between the simulations and laboratory measurements of the pressure and blade vibration accelerations in a hydro turbine passage was obtained, indicating that the GiViRES-Hughes-Newmark algorithm presented in this paper is suitable for dealing with the flow-induced vibration of structures under small deformation. 展开更多
关键词 flow-induced vibration fluid-structure interaction generalized variationalprinciple numerical methods generalized minimum residual (GMRES) method
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Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities 被引量:1
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作者 N.M.BUJURKE M.H.KANTLI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第6期881-898,共18页
This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized... This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest. 展开更多
关键词 transient elastohydrodynamic lubrication(EHL) surface roughness bearing Newton-Krylov method generalized minimal residual(GMRES) wavelet preconditioner
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A KIND OF GENERAL INFLUENCE MEASURE ON THE LINEAR WEIGHTED REGRESSION
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作者 杨虎 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第9期877-881,共5页
The linear weighted regression model is one of the models studied in many articles in recent years. Some further problems, such as disturbation, influence measure and estimate efficiency, have been discussed in this p... The linear weighted regression model is one of the models studied in many articles in recent years. Some further problems, such as disturbation, influence measure and estimate efficiency, have been discussed in this paper on the basis of the regression diagnosties. The partial conclusions of this paper are the extension of the familiar concepts in the regression diagnosties theory[2' 3,7] because they are representative of this kind of model. 展开更多
关键词 heteroscedastic regression diagnostic efficiency generalized student's residual influence measure
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Projection Improved SPAI Preconditioner for FGMRES
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作者 Mingguang Geng Shuli Sun 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2023年第4期1035-1052,共18页
Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for a... Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all problems.In this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of iteration.The proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the matrices.The strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable one.The paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different applications.The results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems. 展开更多
关键词 Generalized minimal residual PRECONDITIONER sparse approximate inverse oblique projection orthogonal projection
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Mathematical Programming Solution for the Frictional Contact Multipole BEM 被引量:8
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作者 于春肖 申光宪 刘德义 《Tsinghua Science and Technology》 SCIE EI CAS 2005年第1期51-56,共6页
This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with frict... This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM. 展开更多
关键词 nonlinear programming generalized minimal residual algorithm (GMRES(m)) point-to-surface contact multipole boundary element method
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PRESSURE CORRECTION METHOD ON UNSTRUCTURED GRIDS 被引量:9
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作者 LAIXi-jun WANGDe-guan CHENYang 《Journal of Hydrodynamics》 SCIE EI CSCD 2004年第3期316-324,共9页
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
关键词 finite volume method unstructured grids generalized minimum residual(GMRES) method incomplete LU (ILU) preconditioner
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Helmholtz Solving and Performance Optimization in Global/Regional Assimilation and Prediction System 被引量:2
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作者 Jianqiang Huang Wei Xue +3 位作者 Haodong Bian Wenxin Yan Xiaoying Wang Wenguang Chen 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2021年第3期335-346,共12页
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
关键词 Global/Regional Assimilation and Prediction System(GRAPES) Helmholtz equation Generalized Conjugate residual(GCR) performance optimization Incomplete LU(ILU)
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Extending GCR Algorithm for the Least Squares Solutions on a Class of Sylvester Matrix Equations
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作者 Baohua Huang Changfeng Ma 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2018年第1期140-159,共20页
The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the l... The purpose of this paper is to derive the generalized conjugate residual(GCR)algorithm for finding the least squares solution on a class of Sylvester matrix equations.We prove that if the system is inconsistent,the least squares solution can be obtained within finite iterative steps in the absence of round-off errors.Furthermore,we provide a method for choosing the initial matrix to obtain the minimum norm least squares solution of the problem.Finally,we give some numerical examples to illustrate the performance of GCR algorithm. 展开更多
关键词 Sylvester matrix equation Least squares solution Generalized conjugate residual algorithm Numerical experiments
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Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations
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作者 Xuejuan Chen Zhiping Mao George Em Karniadakis 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2022年第4期876-902,共27页
We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically... We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically,we discretize the resulted Picard integral equation by the SDC method and accelerate the convergence of the SDC iteration by using the generalized minimal residual algorithm(GMRES).We first derive the correction matrix of the SDC method for FDEs and analyze the convergence region of the SDC method.We then present several numerical examples for stiff and non-stiff FDEs including fractional linear and nonlinear ODEs as well as fractional phase field models,demonstrating that the accelerated SDC method is much more efficient than the original SDC method,especially for stiff problems.Furthermore,we resolve the issue of low accuracy arising from the singularity of the solutions by using a geometric mesh,leading to highly accurate solutions compared to uniform mesh solutions at almost the same computational cost.Moreover,for long-time integration of FDEs,using the geometric mesh leads to great computational savings as the total number of degrees of freedom required is relatively small. 展开更多
关键词 Stiff problem generalized minimal residual geometric mesh refinement long time evolution fractional phase field models
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Implicit Parallel FEM Analysis of Shallow Water Equations
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作者 江春波 李凯 +1 位作者 刘宁 张庆海 《Tsinghua Science and Technology》 SCIE EI CAS 2005年第3期364-371,共8页
The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The sh... The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The shallow water equation was discretized to a linear system of equations with a direct parallel generalized minimum residual algorithm (GMRES) used to solve the linear system. Unlike other parallel GMRES methods, the direct GMRES method does not alter the sequential algorithm, but bases the paral- lelization on basic operations such as the matrix-vector product. The computed results agree well with ob- served results. The parallel computing technique significantly increases the solution speed for this large- scale problem. 展开更多
关键词 shallow water equations parallel computing generalized minimum residual algorithm (GMRES)
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