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Exponential time differencing based efficient SC-PML for RCS simulation 认领 引用 被引量：3
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作者 NIU Liqiang XIE Yongjun +1 位作者 JIANG Haolin WU Peiyu 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2020年第4期703-711,共9页
To efficiently simulate and calculate the radar cross section(RCS) related electromagnetic problems by employing the finite-difference time-domain(FDTD) algorithm, an efficient stretched coordinate perfectly matched l... To efficiently simulate and calculate the radar cross section(RCS) related electromagnetic problems by employing the finite-difference time-domain(FDTD) algorithm, an efficient stretched coordinate perfectly matched layer(ESC-PML) based upon the exponential time differencing(ETD) method is proposed.The proposed implementation can not only reduce the number of auxiliary variables in the SC-PML regions but also maintain the ability of the original SC-PML in terms of the absorbing performance. Compared with the other existed algorithms, the ETDFDTD method shows the least memory consumption resulting in the computational efficiency. The effectiveness and efficiency of the proposed ESC-PML scheme is verified through the RCS relevant problems including the perfect E conductor(PEC) sphere model and the patch antenna model. The results indicate that the proposed scheme has the advantages of the ETD-FDTD method and ESC-PML scheme in terms of high computational efficiency and considerable computational accuracy. 展开更多
关键词 exponential time differencing(ETD) efficient stretched coordinate(ESC) finite-difference time-domain(FDTD) perfectly matched layer(PML) radar cross section(RCS)
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Image Steganography by Pixel-Value Differencing Using General Quantization Ranges 认领 引用 被引量：2
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作者 Da-Chun Wu Zong-Nan Shih 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期353-383,共31页
A new steganographic method by pixel-value differencing(PVD)using general quantization ranges of pixel pairs’difference values is proposed.The objective of this method is to provide a data embedding technique with a ... A new steganographic method by pixel-value differencing(PVD)using general quantization ranges of pixel pairs’difference values is proposed.The objective of this method is to provide a data embedding technique with a range table with range widths not limited to powers of 2,extending PVD-based methods to enhance their flexibility and data-embedding rates without changing their capabilities to resist security attacks.Specifically,the conventional PVD technique partitions a grayscale image into 1×2 non-overlapping blocks.The entire range[0,255]of all possible absolute values of the pixel pairs’grayscale differences in the blocks is divided into multiple quantization ranges.The width of each quantization range is a power of two to facilitate the direct embedding of the bit information with high embedding rates.Without using power-of-two range widths,the embedding rates can drop using conventional embedding techniques.In contrast,the proposed method uses general quantization range widths,and a multiple-based number conversion mechanism is employed skillfully to implement the use of nonpower-of-two range widths,with each pixel pair being employed to embed a digit in the multiple-based number.All the message bits are converted into a big multiple-based number whose digits can be embedded into the pixel pairs with a higher embedding rate.Good experimental results showed the feasibility of the proposed method and its resistance to security attacks.In addition,implementation examples are provided,where the proposed method adopts non-power-of-two range widths and employsmultiple-based number conversion to expand the data-hiding and steganalysis-resisting capabilities of other PVD methods. 展开更多
关键词 Steganography pixel-value differencing multiple-based number conversion general quantization range
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New Predictor-Corrector Methods Based on Exponential Time Differencing forSystems of Nonlinear Differential Equations 认领 引用 被引量：1
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作者 TANGChen YANHai-Qing ZHANGHao LIWen-Run LIUMing ZHANGGui-Min 《Communications in Theoretical Physics》 SCIE CAS 2004年第2期219-224,共6页
We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponent... We present the new predictor-corrector methods for systems of nonlinear differential equations, based on the method of exponential time differencing. We compare the present schemes with the explicit multistep exponential time differencing and Adams–Bashforth–Moulton method. The numerical results show that the schemes are more accurate and more efficient than Adams predictor-corrector method. The exponential time differencing method has been developed and perfected by the present studies. 展开更多
关键词 predictor-corrector methods of exponential time differencing nonlinear system chaos
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A Homogenized Function to Recover Wave Source by Solving a Small Scale Linear System of Differencing Equations 认领 引用
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作者 Chein-Shan Liu Wen Chen Ji Lin 《Computer Modeling in Engineering & Sciences》 SCIE EI 2016年第5期421-435,共15页
In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can si... In order to recover unknown space-dependent function G(x)or unknown time-dependent function H(t)in the wave source F(x;t)=G(x)H(t),we develop a technique of homogenized function and differencing equations,which can significantly reduce the difficulty in the inverse wave source recovery problem,only needing to solve a few equations in the problem domain,since the initial condition/boundary conditions and a supplementary final time condition are satisfied automatically.As a consequence,the eigenfunctions are used to expand the trial solutions,and then a small scale linear system is solved to determine the expansion coefficients from the differencing equations.Because the ill-posedness of the inverse wave source problem is greatly reduced,the present method is accurate and stable against a large noise up to 50%,of which the numerical tests confirm the observation. 展开更多
关键词 Wave source recovery problem Eigenfunctions Homogenized function Differencing equations
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Multi-channel differencing adaptive noise cancellation with multi-kernel method 认领 引用 被引量：1
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作者 Wei Gao Jianguo Huang Jing Han 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2015年第3期421-430,共10页
Although a various of existing techniques are able to improve the performance of detection of the weak interesting sig- nal, how to adaptively and efficiently attenuate the intricate noises especially in the case of n... Although a various of existing techniques are able to improve the performance of detection of the weak interesting sig- nal, how to adaptively and efficiently attenuate the intricate noises especially in the case of no available reference noise signal is still the bottleneck to be overcome. According to the characteristics of sonar arrays, a multi-channel differencing method is presented to provide the prerequisite reference noise. However, the ingre- dient of obtained reference noise is too complicated to be used to effectively reduce the interference noise only using the clas- sical linear cancellation methods. Hence, a novel adaptive noise cancellation method based on the multi-kernel normalized least- mean-square algorithm consisting of weighted linear and Gaussian kernel functions is proposed, which allows to simultaneously con- sider the cancellation of linear and nonlinear components in the reference noise. The simulation results demonstrate that the out- put signal-to-noise ratio （SNR） of the novel multi-kernel adaptive filtering method outperforms the conventional linear normalized least-mean-square method and the mono-kernel normalized least- mean-square method using the realistic noise data measured in the lake experiment. 展开更多
关键词 adaptive noise cancellation multi-channel differencing multi-kernel learning array signal processing.
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Voltage-Mode Universal Biquad Filter Employing Single Voltage Differencing Differential Input Buffered Amplifier 认领 引用 被引量：2
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作者 Kanhaiya Lal Pushkar Data Ram Bhaskar Dinesh Prasad 《Circuits and Systems》 2013年第1期44-48,共5页
A new multi function voltage-mode universal biquadratic filter using single Voltage Differencing Differential Input Buffered Amplifier (VD-DIBA), two capacitors and one resistor is proposed. The proposed configuration... A new multi function voltage-mode universal biquadratic filter using single Voltage Differencing Differential Input Buffered Amplifier (VD-DIBA), two capacitors and one resistor is proposed. The proposed configuration has four inputs and one output and can realize all the five standard filters from the same circuit configuration. The presented biquad filter offers low active and passive sensitivities. The validity of proposed universal biquadratic filter has been verified by SPICE simulation using 0.35 μm MIETEC technology. 展开更多
关键词 Voltage Differencing Differential Input Buffered Amplifier Analog Filter Voltage-Mode
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Block-Based Steganographic Algorithm Using Modulus Function and Pixel-Value Differencing 认领 引用 被引量：3
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作者 Ahlam K. Al-Dhamari Khalid A. Darabkh 《Journal of Software Engineering and Applications》 2017年第1期56-77,共22页
The main purpose in developing the steganographic algorithms lies in achieving most of the steganographic objectives which comprise the embedding capacity, imperceptibility, security, robustness and complexity. In thi... The main purpose in developing the steganographic algorithms lies in achieving most of the steganographic objectives which comprise the embedding capacity, imperceptibility, security, robustness and complexity. In this paper, we propose a high quality steganographic algorithm using new block structure which makes a good use of both modulus function and pixel-value differencing, namely, MF-PVD. We have made many experiments with various test images from several galleries, such as USC-SIPI and UWATERLOO-LINK. The performance of our proposed algorithm is verified using three different performance metrics which include peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and embedding capacity (EC). Experimental results and comparisons with six pertinent state-of-art algorithms are given to prove the validation and efficiency of the proposed algorithm. 展开更多
关键词 Data Hiding Steganography Watermarking Pixel-Value Differencing Modulus Function Performance Metrics
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New Voltage Mode Sinusoidal Oscillator Using Voltage Differencing Transconductance Amplifiers (VDTAs) 认领 引用
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作者 Nisha Walde Syed Naseem Ahmad 《Circuits and Systems》 2015年第8期173-178,共6页
The purpose of this paper is to introduce a new electronically controlled voltage mode sinusoidal oscillator (VMSO) using Voltage Differencing Transconductance Amplifiers (VDTA). The proposed circuit provides electron... The purpose of this paper is to introduce a new electronically controlled voltage mode sinusoidal oscillator (VMSO) using Voltage Differencing Transconductance Amplifiers (VDTA). The proposed circuit provides electronic control of ω0 and independent condition of oscillation (CO). It is found that the oscillator works very satisfactorily and pure sinusoidal waveforms are available at the outputs. The PSPICE simulation confirms the theoretical results. The proposed oscillator circuit employs only two VDTAs, along with two grounded capacitor and single grounded resistor. The circuit exhibits low active and passive sensitivities for ω0. Simulation results are obtained by using PSPICE software with TSMC CMOS 0.18 um process parameters. 展开更多
关键词 Voltage Differencing Transconductance Amplifier (VDTA) Voltage-Mode Circuit Oscillator
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Multifunction Filter Employing Current Differencing Buffered Amplifier 认领 引用
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作者 Tajinder Singh Arora Udit Rana 《Circuits and Systems》 2016年第5期543-550,共8页
This paper proposes a new filter biquad circuit, which utilizes three Current Differencing Buffered Amplifiers (CDBA), two capacitors and five resistors, and operates in the trans-resistance mode. This multi-input and... This paper proposes a new filter biquad circuit, which utilizes three Current Differencing Buffered Amplifiers (CDBA), two capacitors and five resistors, and operates in the trans-resistance mode. This multi-input and single-output multifunction filter uses only grounded capacitors. All the employed resistors are either grounded or virtually grounded, which is an important parameter for its implementation as an integrated circuit. The circuit enjoys independent tunability of angular frequency and bandwidth. The 0.5 μm technology process parameters have been utilized to test and verify the performance characteristics of the circuit using PSPICE. The non-ideal analysis and sensitivity analysis, transient response, Monte-Carlo analysis and calculations of total harmonic distortion have also been shown. 展开更多
关键词 Active Filters Current Differencing Buffered Amplifier Biquadratic Filter KHN-Biquad
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Temporal modulation and frame-differencing enhanced high-density super-resolution optical fluctuation imaging 认领 引用
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作者 DUANTAO HOU LIWEN CHEN +6 位作者 ZHIJIA LIU KEDONG OUYANG YIAN ZHU LONGFANG YAO YIYAN FEI LAN MI JIONG MA 《Photonics Research》 SCIE EI CAS CSCD 2026年第4期1568-1587,共20页
Super-resolution microscopy has enabled nanoscale imaging beyond the diffraction limit.Among various techniques,super-resolution optical fluctuation imaging(SOFI)is notable for its hardware simplicity and suitability ... Super-resolution microscopy has enabled nanoscale imaging beyond the diffraction limit.Among various techniques,super-resolution optical fluctuation imaging(SOFI)is notable for its hardware simplicity and suitability for live-cell imaging.However,under high fluorescent labeling density,SOFI reconstructions often suffer from reduced resolution and imaging artifacts.This study proposes a super-resolution optical fluctuation imaging approach based on temporal modulation and frame-differencing(dSOFI).By employing periodic photoactivation to modulate fluorophore density and introducing a frame-differencing algorithm,dSOFI effectively reduces molecular density during the reconstruction process.The method demonstrates broad compatibility across sample types,imaging modes,and post-processing algorithms.When integrated with the commercial spinning-disk confocal system,dSOFI achieves a lateral resolution of 72 nm in live-cell imaging,and reveals a potential upper bound of lateral resolution approaching~60 nm under well-controlled acquisition conditions when combined with sparse deconvolution.dSOFI provides a broadly applicable and easy-to-implement solution for high-density super-resolution imaging,particularly under live-cell conditions. 展开更多
关键词 DSOFI high density imaging SOFI super resolution optical fluctuation imaging nanoscale imaging frame differencing temporal modulation super resolution microscopy
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Maximum bound principle preserving exponential time differencing schemes for the penalized Allen-Cahn-Ohta-Kawasaki model 认领 引用
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作者 Yingying Wang Xiao Li Zhengru Zhang 《Science China Mathematics》 SCIE CSCD 2026年第3期835-856,共22页
The nonlocal penalized Allen-Cahn-Ohta-Kawasaki(pACOK)equation,equipped with a specific nonlinear function in the Ohta-Kawasaki free energy functional,satisfies the maximum bound principle(MBP).In this paper,we develo... The nonlocal penalized Allen-Cahn-Ohta-Kawasaki(pACOK)equation,equipped with a specific nonlinear function in the Ohta-Kawasaki free energy functional,satisfies the maximum bound principle(MBP).In this paper,we develop and analyze the first-and second-order exponential time differencing(ETD)schemes for solving the p ACOK equation.The fully discrete numerical schemes are obtained by adopting the second-order central difference approximation in space.This is an initial exploration of the application of the ETD schemes on the p ACOK equation and,to the best of our knowledge,also the first work on the second-order linear scheme for this model with the complete theoretical proofs of the MBP preservation and unconditional energy stability.In addition,numerical experiments convincingly demonstrate superior accuracy and faster convergence rates of the proposed ETD schemes compared with the existing stabilized linear schemes.Furthermore,we simulate various microstructures of diblock copolymers. 展开更多
关键词 penalized Allen-Cahn-Ohta-Kawasaki equation exponential time differencing maximum bound principle energy stability diblock copolymers
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Note on Filon-type integration for higher order exponential time differencing methods in stiff systems 认领 引用
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作者 XIANG Shu-huang 《Journal of Central South University of Technology》 2005年第Z1期298-303,共6页
The Filon-type quadrature is efficient for highly oscillatory functions - Fourier transforms. Based on Cox and Matthews' ETD schemes, the higher order single step exponential time differencing schemes are presente... The Filon-type quadrature is efficient for highly oscillatory functions - Fourier transforms. Based on Cox and Matthews' ETD schemes, the higher order single step exponential time differencing schemes are presented based on the Filon-type integration and the A-stability of the two-order Adams-Bashforth exponential time differencing scheme is considered. The effectiveness and accuracy of the schemes is tested. 展开更多
关键词 exponential time differencing method stiff system Filon method Runge-Kutta method
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Higher-order energy-decreasing exponential time differencing Runge-Kutta methods for gradient flows 认领 引用
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作者 Zhaohui Fu Jie Shen Jiang Yang 《Science China Mathematics》 SCIE CSCD 2025年第7期1727-1746,共20页
In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,... In this paper,we develop a general framework for constructing higher-order,unconditionally energydecreasing exponential time differencing Runge-Kutta(ETDRK)methods applicable to a range of gradient flows.Specifically,we identify conditions sufficient for ETDRK schemes to maintain the original energy dissipation.Our analysis reveals that the widely-employed third-and fourth-order ETDRK schemes fail to meet these conditions.To address this,we introduce new third-order ETDRK schemes,designed with appropriate stabilization,which satisfy these conditions and thus guarantee the unconditional energy decay property.We conduct extensive numerical experiments with these new schemes to verify their accuracy,stability,behavior under large time steps,long-term evolution,and adaptive time-stepping strategy across various gradient flows.This study offers the first framework to examine the unconditional energy stability of high-order ETDRK methods,and we are optimistic that our framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable. 展开更多
关键词 exponential time differencing Runge-Kutta method energy stability gradient flows phase-field models
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Learnable differencing center for nighttime depth perception 认领 引用
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作者 Zhiqiang Yan Yupeng Zheng +3 位作者 Deng-Ping Fan Xiang Li Jun Li Jian Yang 《Visual Intelligence》 2024年第1期172-183,共12页
Depth completion is the task of recovering dense depth map from sparse ones,usually with the help of color images.Existing image guided methods perform well on daytime depth perception self-driving benchmarks,but stru... Depth completion is the task of recovering dense depth map from sparse ones,usually with the help of color images.Existing image guided methods perform well on daytime depth perception self-driving benchmarks,but struggle in nighttime scenarios with poor visibility and complex illumination.To address these challenges,we propose a simple yet effective learnable differencing center network(LDCNet).The key idea is to use recurrent inter-convolution differencing(RICD)and illumination affinitive intra-convolution differencing(IAICD)to enhance the nighttime color images and reduce the negative effects of the varying illumination,respectively.RICD explicitly estimates global illumination by differencing two convolutions with different kernels,treating the small-kernel-convolution feature as the center of the large-kernel-convolution feature in a new perspective.IAICD softly alleviates the local relative light intensity by differencing a single convolution,where the center is dynamically aggregated based on neighboring pixels and the estimated illumination map in the RICD.On both nighttime depth completion and depth estimation tasks,extensive experiments demonstrate the effectiveness of our LDCNet,reaching the state of the art. 展开更多
关键词 Nighttime depth perception Learnable differencing center Inter-convolution differencing Intra-convolution differencing
Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study 认领 引用 被引量：6
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作者 Xucheng Meng Thi-Thao-Phuong Hoang +1 位作者 Zhu Wang Lili Ju 《Communications in Computational Physics》 SCIE 2021年第1期80-110,共31页
In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water equations.Comparing with explicit time stepping of the same order accuracy in time,the... In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water equations.Comparing with explicit time stepping of the same order accuracy in time,the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability.To accelerate the ETD simulations,we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition.By dividing the original problem into many subdomain problems of smaller sizes and solving them locally,the proposed approach could speed up the calculation of matrix exponential vector products.Several standard test cases for shallow water equations of one or multiple layers are considered.The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step. 展开更多
关键词 Exponential time differencing domain decomposition rotating shallow water equa-tions finite volume discretization
Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle 认领 引用 被引量：2
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作者 Qiumei Huang Kun Jiang Jingwei Li 《Advances in Applied Mathematics and Mechanics》 SCIE 2022年第2期494-527,共34页
The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a... The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of ma-terials.It has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation law.Based on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efficientfirst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of state.Convergence analyses as well as energy stability are also proven.Several two-dimensional and three-dimensional experiments are performed to verify these theo-retical results. 展开更多
关键词 Peng-Robinson equation of state diffuse interface model maximum bound principle exponential time differencing Lagrange multiplier
Dark-field detection method of shallow scratches on the super-smooth optical surface based on the technology of adaptive smoothing and morphological differencing 认领 引用 被引量：2
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作者 李晨 杨甬英 +9 位作者 柴惠婷 张毅晖 吴凡 周林 闫凯 白剑 沈亦兵 许乔 姜宏振 刘旭 《Chinese Optics Letters》 SCIE EI CAS CSCD 2017年第8期53-57,共5页
In recent years, modern optical processing technologies, such as single point diamond turning, ion beam etching, and magneto-theological finishing, arc getting break- throughs. Machining precisions of super-smooth opt... In recent years, modern optical processing technologies, such as single point diamond turning, ion beam etching, and magneto-theological finishing, arc getting break- throughs. Machining precisions of super-smooth optics have also been significantly improved. However, with increasing demands for the optical surface quality, 展开更多
关键词 Dark-field detection method of shallow scratches on the super-smooth optical surface based on the technology of adaptive smoothing and morphological differencing
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DOA estimation in unknown colored noise using covariance differencing and sparse signal recovery 认领 引用 被引量：1
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作者 TIAN Ye SUN Xiao-ying QIN Yu-di 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2014年第3期106-112,共7页
A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of ... A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources. 展开更多
关键词 direction-of-arrival covariance differencing sparse signal recovery reweighted 21-norm penalty unknown covariance
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Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem without Slope Selection 认领 引用 被引量：1
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作者 Danni Zhang Ruihan Guo 《Advances in Applied Mathematics and Mechanics》 SCIE 2023年第3期545-567,共23页
In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restric... In this paper,we prove the optimal error estimates in L2 norm of the semidiscrete local discontinuous Galerkin(LDG)method for the thin film epitaxy problem without slope selection.To relax the severe time step restriction of explicit time marching methods,we employ a class of exponential time differencing(ETD)schemes for time integration,which is based on a linear convex splitting principle.Numerical experiments of the accuracy and long time simulations are given to show the efficiency and capability of the proposed numerical schemes. 展开更多
关键词 Local discontinuous Galerkin method thin film epitaxy problem error estimates exponential time differencing long time simulation
BOX-LINE RELAXATION SCHEMES FOR SOLVING THE STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS USING SECOND-ORDER UPWIND DIFFERENCING 认领 引用
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作者 Zhang Lin-bo 《Journal of Computational Mathematics》 SCIE 1995年第1期32-39,共8页
We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding ... We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented 展开更多
关键词 line BOX-LINE RELAXATION SCHEMES FOR SOLVING THE STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS USING SECOND-ORDER UPWIND DIFFERENCING LINE Zhang St
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