Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs

Guan Hongbo; Wang Yong; Zhu Huiqing

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Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs

机译：用于求解Dirichlet边界的无丝石方法，由椭圆PDE控制的最佳控制问题

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摘要

In this paper, two meshless schemes are proposed for solving Dirichlet boundary optimal control problems governed by elliptic equations. The first scheme uses radial basis function collocation method (RBF-CM) for both state equation and adjoint state equation, while the second scheme employs the method of fundamental solution (MFS) for the state equation when it has a zero source term, and RBF-CM for the adjoint state equation. Numerical examples are provided to validate the efficiency of the proposed schemes. (C) 2019 Elsevier Ltd. All rights reserved.

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来源
《Applied mathematics letters》 |2019年第2019期|共8页
作者
Guan Hongbo; Wang Yong; Zhu Huiqing;
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作者单位

Zhengzhou Univ Light Ind Coll Math &

Informat Sci Zhengzhou Henan Peoples R China;

Washington Univ Dept Obstet &

Gynecol Radiol Biomed Engn St Louis MO 63110 USA;

Univ Southern Mississippi Sch Math &

Nat Sci Hattiesburg MS 39406 USA;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Boundary optimal control problems; Radial basis functions; Collocation method; Method of fundamental solution;

机译：边界最优控制问题;径向基函数;搭配方法;基本解决方法;

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专利

1. Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs [J] . Guan Hongbo, Wang Yong, Zhu Huiqing Applied mathematics letters . 2019,第期

机译：用于求解Dirichlet边界的无丝石方法，由椭圆PDE控制的最佳控制问题
2. MIXED FINITE ELEMENT METHOD FOR DIRICHLET BOUNDARYCONTROL PROBLEM GOVERNED BY ELLIPTIC PDES [J] . WEI GONG, NINGNING YAN SIAM Journal on Control and Optimization . 2011,第3期

机译：椭圆Pdes控制Dirichlet边界控制问题的混合有限元方法
3. Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs [J] . Gong Wei, Hinze Michael, Zhou Zhaojie Journal of Scientific Computing . 2016,第3期

机译：抛物型偏微分方程控制Dirichlet边界控制问题的有限元方法和先验误差估计
4. Combination approach of domain-type and boundary-type meshless methods for solving hybrid boundary-value problem of homogeneous and inhomogeneous elliptic PDEs [C] . Ayumu Saitoh, Teruou Takayama, Atsushi Kamitani Biennial IEEE Conference on Electromagnetic Field Computation . 2016

机译：域类型和边界类型无网格方法的组合方法，用于求解均质和非均质椭圆形偏微分方程的混合边值问题
5. Meshless Methods for Numerically Solving Boundary Value Problems of Elliptic Type Partial Differential Equations [D] . Choi, Minhwa 2018

机译：数值求解椭圆型偏微分方程边值问题的无网格方法
6. Assumption of Boundary Values and the Greens Function in the Dirichlet Problem for the General Linear Elliptic Equation [O] . Felix E. Browder 1953

机译：一般线性椭圆型方程Dirichlet问题中的边值和格林函数的假设
7. Preconditioned Dirichlet-Dirichlet Methods for Optimal Control of Elliptic PDE [O] . Daniel Loghin 2018

机译：用于最佳控制的预处理Dirichlet-Dirichlet方法椭圆PDE的最佳控制

Meshless methods for solving Dirichlet boundary optimal control problems governed by elliptic PDEs

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