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A numerical algorithm for a class of BSDEs via the branching process

STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2014年第2期124卷 1112-1140页

作者： Henry-Labordere, Pierre Tan, Xiaolu Touzi, Nizar Univ Paris 09 CEREMADE F-75775 Paris 16 France Ecole Polytech Paris Ctr Math Appl Paris France

We give a study to the algorithm for semi-linear parabolic PDEs in Henry-Labordere (2012) and then generalize it to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren et al. (to appear) [5] and extended in Ekren et al. (2012) [6,7]. (C) 2013 Elsevier B.V. All rights reserved.

关键词： numerical algorithm BSDEs Branching process Viscosity solution Path dependent PDEs

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A novel fast numerical algorithm for cascaded Raman fiber laser using the analytic approximate solution

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OPTICS COMMUNICATIONS 2007年第1期271卷 257-262页

作者： Huang Kaidi Zhou Xiaojun Qin Zujun Wu Haocheng Zhou Zili Univ Elect Sci & Technol China Sch Optoelect Informat Chengdu 610054 Peoples R China Guilin Inst Opt Commun Guilin 541004 Peoples R China

In this paper, we proposed a novel numerical algorithm for cascaded Raman fiber laser (CRFL) using the approximate analytic results as the initial values for shooting method, which effectively reduces the calculating time from several hours to a few minutes. With the algorithm, we obtained a numerical solution of the bilateral-pumping Ge-doped fifth-order CRFL which can avoid the so-called "end face damage" phenomenon efficiently. At the same time, we also simulated the unilateral-pumping one as a comparison, which showed both the characteristics of them are similar with each other. (c) 2006 Elsevier B.V. All rights reserved.

关键词： cascaded fiber Raman laser numerical algorithm shooting bilateral pump

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An iterative numerical algorithm for modeling a class of Wiener nonlinear systems

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APPLIED MATHEMATICS LETTERS 2013年第4期26卷 487-493页

作者： Xiong, Weili Ma, Junxia Ding, Ruifeng Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China

This letter presents an iterative estimation algorithm for modeling a class of output nonlinear systems. The basic idea is to derive an estimation model and to solve an optimization problem using the gradient search. The proposed iterative numerical algorithm can estimate the parameters of a class of Wiener nonlinear systems from input-output measurement data. The proposed algorithm has faster convergence rates compared with the stochastic gradient algorithm. The numerical simulation results indicate that the proposed algorithm works well. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： System modeling numerical algorithm Gradient search Parameter estimation Wiener nonlinear system

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numerical evaluation on the effective thermal conductivity of the composites with discontinuous inclusions: Periodic boundary condition and its numerical algorithm

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2019年 134卷 735-751页

作者： Tian, Wenlong Qi, Lehua Chao, Xujiang Liang, Junhao Fu, M. W. Northwestern Polytech Univ Sch Mech Engn Xian 710072 Shaanxi Peoples R China Hong Kong Polytech Univ Dept Mech Engn Hung Hom Hong Kong Peoples R China Northwestern Polytech Univ Sch Mat Sci & Engn Xian 710072 Shaanxi Peoples R China

Boundary condition plays an important role in prediction of the effective thermal conductivity of composites. In this research, the periodic boundary condition and the representative volume element (RVE) based finite element (FE) homogenization method are adopted to evaluate the effective thermal conductivities of the composites reinforced by the spherical, ellipsoidal and cylindrical inclusions, and the emphases are on the numerical implementation algorithm and validation of the periodic boundary condition. The heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites is analyzed and the effective thermal conductivity of the composites are homogenized. The results show that the heat flux continuity of the node pairs on the opposite surfaces of the RVEs of the composites can be guaranteed by the proposed numerical implementation algorithm for the periodic boundary condition, and that the predicted effective thermal conductivities of the composites agree well with those determined by the Lewis-Nielsen model and the experimental tests. Therefore, the RVE based FE homogenization method with the periodic boundary condition can accurately evaluate the effective thermal conductivity of the composites with discontinuous inclusions. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： FE homogenization Heat flux continuity numerical algorithm Periodic boundary condition Thermal conductivity

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Coupled viscoelastic-viscoplastic modeling of homogeneous and isotropic polymers: numerical algorithm and analytical solutions

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2011年第47-48期200卷 3381-3394页

作者： Miled, B. Doghri, I. Delannay, L. Catholic Univ Louvain Inst Mech Mat & Civil Engn IMMC B-1348 Louvain Belgium

A coupled viscoelastic-viscoplastic (VE-VP) model is implemented and studied. The total strain is the sum of VE and VP parts, and the Cauchy stress is given by a linear YE model as a Boltzmann integral of the history of VE strains. The proposed computational algorithm features fully implicit integration, return mapping based on a two-step YE predictor/VP corrector strategy, and a consistent tangent operator. The algorithm is applied to J(2) VP coupled with VE. Very compact expressions are obtained which are form-identical to classical elasto-viscoplasticity (EVP) provided that the constant linear elastic shear and bulk moduli are replaced with incremental relaxation moduli which are appropriate functions of the time increment. Two different integration methods to obtain the incremental moduli are proposed and assessed. Closed-form solutions for uniaxial tension and simple shear are developed, based on an original solution method for integro-differential equations. The analytical results enable to illustrate the constitutive model and provide unambiguous benchmarks for numerical algorithms. Model predictions are compared with experimental data and reasonable correlation is obtained. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Viscoelasticity Viscoplasticity Isothermal numerical algorithm Analytical solutions

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A Rapid and Robust numerical algorithm for Sensitivity Encoding with Sparsity Constraints: Self-Feeding Sparse SENSE

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MAGNETIC RESONANCE IN MEDICINE 2010年第4期64卷 1078-1088页

作者： Huang, Feng Chen, Yunmei Yin, Wotao Lin, Wei Ye, Xiaojing Guo, Weihong Reykowski, Arne Invivo Corp Adv Concept Dev Gainesville FL 32603 USA Univ Florida Dept Math Gainesville FL 32611 USA Rice Univ Dept Computat & Appl Math Houston TX USA Case Western Reserve Univ Dept Math Cleveland OH 44106 USA

The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors. Magn Reson Med 64:1078-1088, 2010. (C) 2010 WileyLiss, Inc.

关键词： partially parallel imaging g-factor sparsity constraint prior information compressed sensing numerical algorithm

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A numerical algorithm for solving a class of linear nonlocal boundary value problems

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APPLIED MATHEMATICS LETTERS 2010年第9期23卷 997-1002页

作者： Lin, Yingzhen Lin, Jinnan Harbin Inst Technol Weihai Dept Math Harbin 264209 Peoples R China Harbin Inst Technol Weihai Software Coll Harbin 264209 Peoples R China

In order to solve a class of linear nonlocal boundary value problems, a new reproducing kernel space satisfying nonlocal conditions is constructed carefully. This makes it easy to solve the problems. Furthermore, the exact solutions of the problems can be expressed in series form. The numerical results demonstrate that the new method is quite accurate and efficient for solving fourth-order nonlocal boundary value problems. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Nonlocal boundary value problems Higher order differential equations New reproducing kernel space numerical algorithm

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A numerical algorithm for solving a coupled problem of the air-sea-wave interaction

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MATHEMATICAL AND COMPUTER MODELLING 1996年第7期24卷 19-32页

作者： Ly, LN Department of Oceanography Naval Postgraduate School Monterey CA 93943-5100 U.S.A.

The ''partly coupled'' algorithm and numerical schemes are developed to solve a coupled model of air-sea-wave interaction, using the matrix and simple pivotal-condensation methods. The ''partly coupled'' algorithm is used to handle boundary conditions at the air-sea interface to allow for solving systems of the atmospheric and oceanic equations, as two separate systems. This ''partly coupled'' algorithm is simpler, more effective, and requires less computing efforts to solve an air-sea-wave coupled model compared to the ''fully coupled'' algorithm developed by Ly [1] for solving a coupled model of the baroclinic atmospheric and oceanic boundary layers. In the numerical schemes, the buoyancy terms of dissipation and TKE budget equations are used as conditions for rearranging equation coefficient vectors to satisfy stability conditions. The mathematical coupled model of the air-sea-wave system is also presented. The model equations are written in the same form for both atmospheric and oceanic boundary layers, and include equations for momentum, the k-epsilon turbulence scheme, and stratification in the atmospheric and oceanic boundary layers. In the model, ocean wind-induced wave effects are modeled by using boundary conditions for the turbulent energy dissipation at the interface in a k-epsilon turbulence closure of the coupled model. numerical experiments are designed for various geostrophic winds, wave heights, and wave ages under neutral atmospheric stratification to demonstrate an example in solving a coupled model of the air-sea-wave system. The numerical simulations show that surface wind-induced waves have strong effects on the basic physical characteristics of the air-sea system.

关键词： numerical algorithm computing scheme air-sea-wave interaction numerical modeling air-sea boundary layers wind-induced waves

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A new numerical algorithm based on transformed equations and its applications to very low Re fluid flows

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期181卷 619-633页

作者： Xu, H. Barron, R. Zhang, C. Univ Western Ontario Dept Mech & Mat Engn London ON N6A 5B9 Canada Univ Windsor Fluid Dynam Res Inst Windsor ON N9B 3P4 Canada Univ Windsor Dept Mech Automot & Mat Engn Windsor ON N9B 394 Canada

A new numerical algorithm is presented in this study to solve the partial differential equations that govern fluid flows. This new algorithm is based on first transforming the partial differential equations by introducing an exponential function to eliminate the convection terms. A fourth-order central differencing scheme and a second-order central differencing scheme are used to discretize the transformed equations. The algorithm is then applied to simulate fluid flows with exact solutions to validate this new algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. Comparisons against the exact solution are made for the results obtained using the new numerical algorithm as well as the power-law scheme. The comparisons indicate that the present fourth-order scheme performs the best and the present second-order scheme is the next most accurate. (c) 2006 Elsevier Inc. All rights reserved.

关键词： partial differential equation differencing scheme fluid flow numerical algorithm

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A numerical algorithm FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第12期19卷 8602-8616页

作者： Zhao, Bowen Xu, Honglei Teo, Kok Lay Curtin Univ Sch Elect Engn Comp & Math Sci Perth 6102 Australia Sunway Univ Sch Math Sci Kuala Lumpur 47500 Malaysia

In this paper, we consider a general class of discrete-time optimal control problems subject to all-time-step constraints on the state and control variables. The derivations of the gradient formulas for the cost and constraint functions for this constrained discrete-time optimal control problem are rather involved. We present a simple approach to the derivations of these gradient formulas based on reversed automatic differentiation. On this basis, a numerical algorithm is developed to solve this all-time-step constrained discrete-time optimal control problem. We then consider a class of continuous-time optimal control problems subject to continuous state inequality constraints. This constrained continuous-time optimal control problem is discretized into a discrete time optimal control problem with all-time-step constraints using the Euler discretization method. Then, the algorithm developed for constrained discrete time optimal control problem is applied to solve this discretized optimal control problem. numerical examples are presented to verify the applicability of the methods.

关键词： Discrete-time optimal control problem continuous-time optimal con-trol problem automatic differentiation gradient formulas numerical algorithm all-time-step in-equality constraints continuous state inequality constraints

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