This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,...This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.展开更多
视网膜血管的结构和形态是计算机辅助系统诊断眼科疾病的重要依据.针对细小血管分割精度低的问题,提出一种融合残差密集模块与三端注意力模块的改进型U-Net算法.首先,将残差模块与密集模块相结合,充分利用每层的特征,提高网络提取细小...视网膜血管的结构和形态是计算机辅助系统诊断眼科疾病的重要依据.针对细小血管分割精度低的问题,提出一种融合残差密集模块与三端注意力模块的改进型U-Net算法.首先,将残差模块与密集模块相结合,充分利用每层的特征,提高网络提取细小血管特征的能力.在解码阶段引入三端注意力模块,利用空间注意力机制自适应地对特征进行空间校正,抑制背景噪声,突出目标区域.同时,通过多尺度特征融合的方式,利用高级语义特征改善网络对细小血管的分割效果.最后,为获取血管的多尺度特征,在编码-解码网络结构中加入空洞卷积,在不增加参数的情况下增加感受野.基于DRIVE和STARE数据集的实验结果表明,所提出网络的灵敏度、特异性、准确率和AUC(area under curve)分别为81.26%/82.57%、98.20%/98.37%、96.70%/97.51%和98.12%/98.41%,优于现有先进算法.展开更多
Improvement in two aspects is done of the one-level mesoscale numerical model of Mass et al.(1985)and the re- vised model is used to make a simulation of a severe convective weather process in North China,with the res...Improvement in two aspects is done of the one-level mesoscale numerical model of Mass et al.(1985)and the re- vised model is used to make a simulation of a severe convective weather process in North China,with the result showing the pronounced effects of the topography upon the mesoscale systems.展开更多
文摘This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.
文摘视网膜血管的结构和形态是计算机辅助系统诊断眼科疾病的重要依据.针对细小血管分割精度低的问题,提出一种融合残差密集模块与三端注意力模块的改进型U-Net算法.首先,将残差模块与密集模块相结合,充分利用每层的特征,提高网络提取细小血管特征的能力.在解码阶段引入三端注意力模块,利用空间注意力机制自适应地对特征进行空间校正,抑制背景噪声,突出目标区域.同时,通过多尺度特征融合的方式,利用高级语义特征改善网络对细小血管的分割效果.最后,为获取血管的多尺度特征,在编码-解码网络结构中加入空洞卷积,在不增加参数的情况下增加感受野.基于DRIVE和STARE数据集的实验结果表明,所提出网络的灵敏度、特异性、准确率和AUC(area under curve)分别为81.26%/82.57%、98.20%/98.37%、96.70%/97.51%和98.12%/98.41%,优于现有先进算法.
基金supported by the National Natural Science Foundation of China
文摘Improvement in two aspects is done of the one-level mesoscale numerical model of Mass et al.(1985)and the re- vised model is used to make a simulation of a severe convective weather process in North China,with the result showing the pronounced effects of the topography upon the mesoscale systems.