检索结果-南通市图书馆

HOMOTOPY CONTINUATION METHODS FOR STOCHASTIC TWO-POINT BOUNDARY VALUE PROBLEMS DRIVEN BY ADDITIVE NOISES

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2014年第6期32卷 630-642页

作者： yanzhao cao PengWang Xiaoshen Wang Department of Mathematics ~ Statistics Auburn University Auburn AL 368~9-5168 USA and School of Mathematics Jilin University Changchun 130012 China School of Mathematics Jilin University Changchun 130012 China Department of Mathematics and Statistics University of Arkansas at Little Rock Little Rock AR 72204 USA

In this paper the homotopy continuation method for stochastic two-point boundary value problems driven by additive noises is studied. The existence of the solution of the homotopy equation is proved. Numerical schemes are constructed and error estimates are obtained. Numerical experiments demonstrate the effectiveness of the homotopy continu- ation method over other commonly used methods such as the shooting method.

关键词： Stochastic differential equations Homotopy method Shooting method.

Spectral Method for Nonlinear Stochastic Partial Differential Equations of Elliptic Type

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Numerical Mathematics(Theory,Methods and Applications) 2011年第1期4卷 38-52页

作者： yanzhao cao Li Yin Department of Mathematics Auburn UniversityAuburnAL 36849USA LCP Institute of Applied Physics and Computational MathematicsBeijing 100088China

This paper is concerned with the numerical approximations of semi-linear stochastic partial differential equations of elliptic type in ***gence analysis and error estimates are presented for the numerical solutions b... 详细信息

关键词： Stochastic differential equation spectral method error estimates white noise

An Implicit Algorithm of Solving Nonlinear Filtering Problems

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2014年第7期16卷 382-402页

作者： Feng Bao yanzhao cao Xiaoying Han Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA School of Mathematics and Computational Sciences Sun Yat-sen UniversityChina

Nonlinear filter problems arise in many applications such as communications and signal *** used numerical simulation methods include Kalman filter method,particle filter method,*** this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation *** experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.

关键词： Kalman filter particle filter implicit filter Monte Carlomethod stochastic differential equations.

Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modeling using adjoint-state sensitivities

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Science China Earth Sciences 2016年第4期59卷 770-779页

作者： HU Bill X cao yanzhao ZHAO WeiDong BAO Feng School of Water Resources and Environmental Sciences China University of Geosciences Department of Geological Sciences Florida State University Department of Mathematics and Statistics Auburn University School of Mathematics Shandong University

A mathematical optimal control method is developed to identify a hydraulic conductivity distribution in a density dependent flow field. Using a variational method, the adjoint partial differential equations are obtained for the density-dependent state equations used for the saline aquifer water flow. The adjoint equations are numerically solved in through a finite difference method. The developed method is applied to identify the hydraulic conductivity distribution through the numerical solution of an optimal control problem. To demonstrate the effectiveness of the optimal control method, three numerical experiments are conducted with artificial observation data. The results indicate that the developed method has the potential to accurately identify the hydraulic conductivity distribution in a saline water aquifer flow system.

关键词： Variable-density flow Hydraulic conductivity Inverse method Adjoint partial differential equation Submarine groundwater discharge

A Symplectic Based Neural Network Algorithm for Quantum Controls under Uncertainty

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Communications in Computational Physics 2022年第5期31卷 1525-1545页

作者： Jingshi Li Song Chen Lijin Wang yanzhao cao Department of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjingJiangsu210044P.R.China Department of Mathematics&Statistics University of Wisconsin–La CrosseLa CrosseWI54601USA School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049P.R.China Department of Mathematics&Statistics Auburn UniversityAuburnAL36830USA

Robust quantum control with uncertainty plays a crucial role in practical quantum *** paper presents a method for solving a quantum control problem by combining neural network and symplecticfinite difference *** neural network approach provides a framework that is easy to establish and *** the same time,the symplectic methods possess the norm-preserving property for the quantum system to produce a realistic solution in *** construct a general high dimensional quantum optimal control problem to evaluate the proposed method and an approach that combines a neural network with forward Euler’s *** analysis and numerical experiments confirm that the neural network-based symplectic method achieves significantly better accuracy and robustness against noises.

关键词： Quantum(noise)control neural network symplectic methods norm-preservation

A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2023年第10期34卷 1361-1390页

作者： Qiang Li Gang Bao yanzhao cao Junshan Lin Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Mathematics Zhejiang UniversityChina Department of Mathematics and Statistics Auburn UniversityAuburnAL 36849USA

In this work,we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar *** formulate the design problems as random PDE-constrained optimization problems and seek the optimal statistical parameters for the random *** optimizations at fixed frequency as well as at multiple frequencies and multiple incident angles are *** evaluate the gradient of the objective function,we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the *** stochastic gradient descent method evaluates the gradient of the objective function only at a few samples for each iteration,which reduces the computational cost *** numerical experiments are conducted to illustrate the efficiency of the method and significant increases of the absorptance for the optimal random *** also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptions for the random interfaces.

关键词： Optimal design random rough surface solar cell Helmholtz equation stochastic gradient descent method

Operator Splitting and Local Time-Stepping Methods for Transport Problems in Fractured Porous Media

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2023年第10期34卷 1215-1246页

作者： Phuoc-Toan Huynh yanzhao cao Thi-Thao-Phuong Hoang Department of Mathematics and Statistics Auburn UniversityAuburn 36849AlabamaUSA

This paper is concerned with efficient numerical methods for the advectiondiffusion equation in a heterogeneous porous medium containing fractures.A dimensionally reduced fracture model is considered,in which the fracture is represented as an interface between subdomains and is assumed to have larger permeability than the surrounding *** develop three global-in-time domain decomposition methods coupled with operator splitting for the reduced fracture model,where the advection and the diffusion are treated separately by different numerical schemes and with different time ***,smaller time steps can be used in the fracture-interface than in the *** first two methods are based on the physical transmission conditions,while the third one is based on the optimized Schwarz waveform relaxation approach with Ventcel-Robin transmission conditions.A discrete space-time interface system is formulated for each method and is solved iteratively and globally in *** results for two-dimensional problems with various P′eclet numbers and different types of fracture are presented to illustrate and compare the convergence and accuracy in time of the proposed methods with local time stepping.

关键词： Domain decomposition reduced fracture model operator splitting nonconforming time grids time-dependent Steklov-Poincare operator optimized Schwarz waveform relaxation

Well-Posedness and Finite Element Approximations for Elliptic SPDEs with Gaussian Noises

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Mathematical Research 2020年第2期36卷 113-127页

作者： yanzhao cao Jialin Hong Zhihui Liu Department of Mathematics Auburn UniversityAuburnAL 36849USA Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Department of Mathematics The Hong Kong University of Science and TechnologyHong Kong SARChina

The paper studies the well-posedness and optimal error estimates of spectral finite element approximations for the boundary value problems of semi-linear elliptic SPDEs driven by white or colored Gaussian *** noise term is approximated through the spectral projection of the covariance operator,which is not required to be commutative with the Laplacian *** the convergence analysis of SPDEs with the noise terms replaced by the projected noises,the well-posedness of the SPDE is established under certain covariance operator-dependent *** SPDEs with projected noises are then numerically approximated with the finite element method.A general error estimate framework is established for the finite element *** on this framework,optimal error estimates of finite element approximations for elliptic SPDEs driven by power-law noises are *** is shown that with the proposed approach,convergence order of white noise driven SPDEs is improved by half for one-dimensional problems,and by an infinitesimal factor for higher-dimensional problems.

关键词： Elliptic stochastic partial differential equation spectral approximations finite element approximations power-law noise

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

45 MW锅炉DPC控制改造

45 MW锅炉DPC控制改造