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Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense 被引量:1
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作者 M. T. Yassen M. A. Sohaly Islam Elbaz 《American Journal of Computational Mathematics》 2016年第2期66-73,共8页
The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for s... The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section. 展开更多
关键词 Random Partial Differential Equations (RPDEs) Mean Square Sense (m.s) Second Order Random Variable (2r.v.'s) Random crank-nicolson scheme CONVERGENCE CONSISTENCY Stability
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A Note on Crank-Nicolson Scheme for Burgers’ Equation 被引量:5
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作者 Kanti Pandey Lajja Verma 《Applied Mathematics》 2011年第7期883-889,共7页
In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equ... In this work we generate the numerical solutions of the Burgers’ equation by applying the Crank-Nicolson method directly to the Burgers’ equation, i.e., we do not use Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. Absolute error of the present method is compared to the absolute error of the two existing methods for two test problems. The method is also analyzed for a third test problem, nu-merical solutions as well as exact solutions for different values of viscosity are calculated and we find that the numerical solutions are very close to exact solution. 展开更多
关键词 Hopf-Cole Transformation Burgers’ Equation crank-nicolson scheme Nonlinear Partial Differential EQUATIONS
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Optimal Error Estimates of the Crank-Nicolson Scheme for Solving a Kind of Decoupled FBSDEs
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作者 Zhe Wang Yang Li 《Journal of Applied Mathematics and Physics》 2018年第2期338-346,共9页
In this paper, under weak conditions, we theoretically prove the second-order convergence rate of the Crank-Nicolson scheme for solving a kind of decoupled forward-backward stochastic differential equations.
关键词 FORWARD BACKWARD Stochastic Differential Equations SECOND-ORDER scheme Error ESTIMATE Trapezoidal RULE
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Finite Difference Approach for Estimating the Thermal Conductivity by 6-point Crank-Nicolson Scheme
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作者 苏亚欣 杨翔翔 《Journal of Donghua University(English Edition)》 EI CAS 2005年第2期45-49,共5页
Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured ex... Based on inverse heat conduction theory, a theoretical model using 6-point Crank-Nicolson finite difference scheme was used to calculate the thermal conductivity from temperature distribution, which can be measured experimentally. The method is a direct approach of second-order and the key advantage of the present method is that it is not required a priori knowledge of the functional form of the unknown thermal conductivity in the calculation and the thermal parameters are estimated only according to the known temperature distribution. Two cases were numerically calculated and the influence of experimental deviation on the precision of this method was discussed. The comparison of numerical and analytical results showed good agreement. 展开更多
关键词 可逆热传导 导热率 有限差分法 克兰克-尼科尔森格式
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Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations
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作者 Dechao Gao Zeshan Qiu +1 位作者 Lizan Wang Jianxin Li 《Journal of Applied Mathematics and Physics》 2024年第4期1089-1100,共12页
The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference oper... The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective. 展开更多
关键词 crank-nicolson Quasi-Compact scheme Fractional Advection-Diffusion Equations NONLINEAR Stability and Convergence
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抛物型最优控制问题的全离散Crank-Nicolson有限元法
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作者 张馨丹 赵建平 侯延仁 《新疆大学学报(自然科学版中英文)》 CAS 2024年第2期196-205,245,共11页
针对具有积分控制约束的抛物型最优控制问题,提出了一种基于Crank-Nicolson格式的全离散有限元法.使用分段线性有限元对状态进行空间离散,采用Crank-Nicolson格式进行时间离散,对控制变量采用分段线性近似,从而得到离散的最优性系统.证... 针对具有积分控制约束的抛物型最优控制问题,提出了一种基于Crank-Nicolson格式的全离散有限元法.使用分段线性有限元对状态进行空间离散,采用Crank-Nicolson格式进行时间离散,对控制变量采用分段线性近似,从而得到离散的最优性系统.证明了状态变量、伴随状态变量和控制变量的误差估计,并通过数值算例验证理论结果. 展开更多
关键词 抛物型最优控制问题 crank-nicolson格式 最优性系统
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Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate 被引量:1
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作者 Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1405-1425,共21页
This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemi... This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters. 展开更多
关键词 Epidemic model fuzzy rate parameters next generation matrix local stability proposed numerical scheme
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Improvement and security analysis of multi-ring discrete modulation continuous variable quantum secret sharing scheme
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作者 姜欢窈 聂敏 +3 位作者 杨光 孙爱晶 张美玲 裴昌幸 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期189-197,共9页
In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propos... In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme(MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol.We conduct a comprehensive analysis of the improved protocol's performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value. 展开更多
关键词 discrete modulation continuous variable quantum secret sharing scheme
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A Non-Parametric Scheme for Identifying Data Characteristic Based on Curve Similarity Matching
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作者 Quanbo Ge Yang Cheng +3 位作者 Hong Li Ziyi Ye Yi Zhu Gang Yao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第6期1424-1437,共14页
For accurately identifying the distribution charac-teristic of Gaussian-like noises in unmanned aerial vehicle(UAV)state estimation,this paper proposes a non-parametric scheme based on curve similarity matching.In the... For accurately identifying the distribution charac-teristic of Gaussian-like noises in unmanned aerial vehicle(UAV)state estimation,this paper proposes a non-parametric scheme based on curve similarity matching.In the framework of the pro-posed scheme,a Parzen window(kernel density estimation,KDE)method on sliding window technology is applied for roughly esti-mating the sample probability density,a precise data probability density function(PDF)model is constructed with the least square method on K-fold cross validation,and the testing result based on evaluation method is obtained based on some data characteristic analyses of curve shape,abruptness and symmetry.Some com-parison simulations with classical methods and UAV flight exper-iment shows that the proposed scheme has higher recognition accuracy than classical methods for some kinds of Gaussian-like data,which provides better reference for the design of Kalman filter(KF)in complex water environment. 展开更多
关键词 Curve similarity matching Gaussian-like noise non-parametric scheme parzen window.
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A Neural-network-based Alternative Scheme to Include Nonhydrostatic Processes in an Atmospheric Dynamical Core
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作者 Yang XIA Bin WANG +13 位作者 Lijuan LI Li LIU Jianghao LI Li DONG Shiming XU Yiyuan LI Wenwen XIA Wenyu HUANG Juanjuan LIU Yong WANG Hongbo LIU Ye PU Yujun HE Kun XIA 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2024年第6期1083-1099,I0002,I0003,共19页
Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostat... Here,a nonhydrostatic alternative scheme(NAS)is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core.The NAS is designed to replace this solver,which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time.Recent advances in machine learning(ML)provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship.In this study,an ML approach called a neural network(NN)was adopted to select leading input features and develop the NAS.The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting(WRF)model.The forward time difference of the nonhydrostatic tendency was used as the target variable,and the five selected features were the nonhydrostatic tendency at the last time step,and four hydrostatic variables at the current step including geopotential height,pressure in two different forms,and potential temperature,respectively.Finally,a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution,which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency.Corrected by the NN-based NAS,the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias,anomaly root-mean-square error,and the error of the wave spatial pattern,which proves the feasibility and superiority of this scheme. 展开更多
关键词 neural network nonhydrostatic alternative scheme atmospheric model dynamical core
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Verifiable quantum secret sharing scheme based on orthogonal product states
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作者 白晨明 刘璐 张素娟 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期178-187,共10页
In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional produc... In the domain of quantum cryptography,the implementation of quantum secret sharing stands as a pivotal element.In this paper,we propose a novel verifiable quantum secret sharing protocol using the d-dimensional product state and Lagrange interpolation techniques.This protocol is initiated by the dealer Alice,who initially prepares a quantum product state,selected from a predefined set of orthogonal product states within the C~d■C~d framework.Subsequently,the participants execute unitary operations on this product state to recover the underlying secret.Furthermore,we subject the protocol to a rigorous security analysis,considering both eavesdropping attacks and potential dishonesty from the participants.Finally,we conduct a comparative analysis of our protocol against existing schemes.Our scheme exhibits economies of scale by exclusively employing quantum product states,thereby realizing significant cost-efficiency advantages.In terms of access structure,we adopt a(t, n)-threshold architecture,a strategic choice that augments the protocol's practicality and suitability for diverse applications.Furthermore,our protocol includes a rigorous integrity verification mechanism to ensure the honesty and reliability of the participants throughout the execution of the protocol. 展开更多
关键词 quantum secret sharing quantum product state threshold scheme unitary operations
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Quantum-Resistant Multi-Feature Attribute-Based Proxy Re-Encryption Scheme for Cloud Services
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作者 Jinqiu Hou Changgen Peng +1 位作者 Weijie Tan Hongfa Ding 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第1期917-938,共22页
Cloud-based services have powerful storage functions and can provide accurate computation.However,the question of how to guarantee cloud-based services access control and achieve data sharing security has always been ... Cloud-based services have powerful storage functions and can provide accurate computation.However,the question of how to guarantee cloud-based services access control and achieve data sharing security has always been a research highlight.Although the attribute-based proxy re-encryption(ABPRE)schemes based on number theory can solve this problem,it is still difficult to resist quantum attacks and have limited expression capabilities.To address these issues,we present a novel linear secret sharing schemes(LSSS)matrix-based ABPRE scheme with the fine-grained policy on the lattice in the research.Additionally,to detect the activities of illegal proxies,homomorphic signature(HS)technology is introduced to realize the verifiability of re-encryption.Moreover,the non-interactivity,unidirectionality,proxy transparency,multi-use,and anti-quantum attack characteristics of our system are all advantageous.Besides,it can efficiently prevent the loss of processing power brought on by repetitive authorisation and can enable precise and safe data sharing in the cloud.Furthermore,under the standard model,the proposed learning with errors(LWE)-based scheme was proven to be IND-sCPA secure. 展开更多
关键词 LATTICE learning with errors attribute-based proxy re-encryption linear secret sharing schemes
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A Practical Regular LDPC Coded Scheme for Physical-Layer Information Security
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作者 Du Junyi 《China Communications》 SCIE CSCD 2024年第5期190-201,共12页
In this paper,we aim to design a practical low complexity low-density parity-check(LDPC)coded scheme to build a secure open channel and protect information from eavesdropping.To this end,we first propose a punctured L... In this paper,we aim to design a practical low complexity low-density parity-check(LDPC)coded scheme to build a secure open channel and protect information from eavesdropping.To this end,we first propose a punctured LDPC coded scheme,where the information bits in a codeword are punctured and only the parity check bits are transmitted to the receiver.We further propose a notion of check node type distribution and derive multi-edge type extrinsic information transfer functions to estimate the security performance,instead of the well-known weak metric bit error rate.We optimize the check node type distribution in terms of the signal-to-noise ratio(SNR)gap and modify the progressive edge growth algorithm to design finite-length codes.Numerical results show that our proposed scheme can achieve a lower computational complexity and a smaller security gap,compared to the existing scrambling and puncturing schemes. 展开更多
关键词 extrinsic information transfer function physical layer scheme secure open channel security gap
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Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes
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作者 Tingting Li Jianfang Lu Pengde Wang 《Communications on Applied Mathematics and Computation》 EI 2024年第1期142-189,共48页
This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary ... This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms. 展开更多
关键词 Compact scheme Diffusion operators Inverse Lax-Wendroff(ILW) Fourier analysis Eigenvalue analysis
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High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings
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作者 Zheng Chen Lin Mu 《Communications on Applied Mathematics and Computation》 EI 2024年第1期325-339,共15页
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g... In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property. 展开更多
关键词 Stochastic Galerkin scheme linear transport equations generalized polynomial approach stochastic asymptotic-preserving property
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A New Double Layer Multi-Secret Sharing Scheme
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作者 Elavarasi Gunasekaran Vanitha Muthuraman 《China Communications》 SCIE CSCD 2024年第1期297-309,共13页
Cryptography is deemed to be the optimum strategy to secure the data privacy in which the data is encoded ahead of time before sharing it.Visual Secret Sharing(VSS)is an encryption method in which the secret message i... Cryptography is deemed to be the optimum strategy to secure the data privacy in which the data is encoded ahead of time before sharing it.Visual Secret Sharing(VSS)is an encryption method in which the secret message is split into at least two trivial images called’shares’to cover it.However,such message are always targeted by hackers or dishonest members who attempt to decrypt the message.This can be avoided by not uncovering the secret message without the universal share when it is presented and is typically taken care of,by the trusted party.Hence,in this paper,an optimal and secure double-layered secret image sharing scheme is proposed.The proposed share creation process contains two layers such as threshold-based secret sharing in the first layer and universal share based secret sharing in the second layer.In first layer,Genetic Algorithm(GA)is applied to find the optimal threshold value based on the randomness of the created shares.Then,in the second layer,a novel design of universal share-based secret share creation method is proposed.Finally,Opposition Whale Optimization Algorithm(OWOA)-based optimal key was generated for rectange block cipher to secure each share.This helped in producing high quality reconstruction images.The researcher achieved average experimental outcomes in terms of PSNR and MSE values equal to 55.154225 and 0.79365625 respectively.The average PSNRwas less(49.134475)and average MSE was high(1)in case of existing methods. 展开更多
关键词 genetic algorithm oppositional whale optimization algorithm rectangle block cipher secret sharing scheme SHARES universal share
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Impacts of Water-Sediment Regulation Scheme on Chromophoric Dissolved Organic Matter in the Lower Yellow River
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作者 LIU Xiao JIANG Xueyan +2 位作者 LIU Qian SUI Juanjuan ZOU Li 《Journal of Ocean University of China》 CAS CSCD 2024年第2期455-466,共12页
As a river with more than 3000 reservoirs in its watershed,the Yellow River has been affected by dams not only on the sediment load,but also on the water quality.Water-sediment regulation scheme(WSRS),which has been c... As a river with more than 3000 reservoirs in its watershed,the Yellow River has been affected by dams not only on the sediment load,but also on the water quality.Water-sediment regulation scheme(WSRS),which has been carried out annually in the Yellow River since 2002,is a typical human activity affecting river water quality.Chromophoric dissolved organic matter(CDOM)in river is susceptible to changes in ecological and environmental conditions as well as human activities.Here,we report variations in dissolved organic carbon concentrations,compositions and sources of CDOM in time series samples in the lower Yellow River during WSRS.In addition,a parallel factor fluorescence analysis(PARAFAC)method is applied to identify different fluorescent components in water samples during WRSR,showing four major components including tryptophan-like component(C1),microbial humic-like component(C2),terrestrial humic-like component(C3)and tyrosine-like component(C4).In general,C1 increased after water regulation,while C2 and C3 increased after sediment regulation,indicating that the water and sediment released by the dam have different effects on CDOM compositions.Under the impacts of the dam,source of CDOM in the lower Yellow River is mainly autochthonous related to microbial activities,and is regulated by the terrestrial input during WSRS period.Sediment resuspension inhibits microbial activities and reduces the production of autochthonous CDOM.Overall,human activities especially WSRS,as exemplified here,significantly alter the quality and quantity of CDOM in the lower Yellow River,affecting CDOM dynamics and biogeochemical processes in the estuarine environment. 展开更多
关键词 chromophoric dissolved organic matter(CDOM) water-sediment regulation scheme(WSRS) Yellow River optical properties
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Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma
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作者 WEN Yi WANG Junxiang XU Hongbing 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2024年第1期65-73,共9页
Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is ... Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation. 展开更多
关键词 anisotropic magnetized plasma body-of-revolution(BOR) crank-nicolson Douglas-Gunn(CNDG) finite-difference time-domain(FDTD) perfectly matched layer(PML) rotationally symmetric multi-scale problems
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Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations
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作者 Zachary M.Miksis Yong-Tao Zhang 《Communications on Applied Mathematics and Computation》 EI 2024年第1期3-29,共27页
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ... Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids. 展开更多
关键词 Fixed-point fast sweeping methods Weighted essentially non-oscillatory(WENO)schemes Sparse grids Static Hamilton-Jacobi(H-J)equations Eikonal equations
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Analysis and Comparison of Slope-cutting Widening Schemes in Highway Reconstruction and Expansion Project Based on MIDAS Software
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作者 Zhiqiang Qiu Yun Shi Lei Jiang 《Journal of Architectural Research and Development》 2024年第2期75-83,共9页
In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the m... In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the main contributor to the stability of the slope.Then,two widening schemes are proposed,which are the steep slope with strong support and the gentle slope with general support schemes.The static/slope module of MIDAS GTS finite element analysis software and the strength reduction method were used to compare the two schemes.The results show that the steep slope with a strong support scheme has obvious advantages in land requisition,environmental protection,and safety and is more suitable for reconstructing and expanding the highway slope. 展开更多
关键词 Highway reconstruction and expansion Slope excavation MIDAS GTS scheme selection
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