A MESHFREE METHOD FOR A PDE-CONSTRAINED OPTIMIZATION PROBLEM

被引：0
|
作者：
Hoff, Daniel [1 ]
Wendland, Holger [2 ]
机构：
[1] Tech Univ Ilmenau, Inst Math, D-98694 Ilmenau, Germany
[2] Univ Bayreuth, Dept Math, Appl & Numer Anal, D-95440 Bayreuth, Germany
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2021年 / 59卷 / 04期
关键词：
PDE-constrained optimization; radial basis functions; meshfree methods; kernel-based approximation; error analysis; SCATTERED-DATA INTERPOLATION; DIVERGENCE-FREE; RADIAL BASIS;
D O I：
10.1137/20M1363510
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We derive an error analysis and give numerical examples.
引用
收藏
页码：1896 / 1917
页数：22
相关论文
共 50 条
  • [1] Adjoint method for a tumor growth PDE-constrained optimization problem
    Knopoff, D. A.
    Fernandez, D. R.
    Torres, G. A.
    Turner, C. V.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (06) : 1104 - 1119
  • [2] Algorithms for PDE-constrained optimization
    Herzog R.
    Kunisch K.
    GAMM Mitteilungen, 2010, 33 (02) : 163 - 176
  • [3] A penalty method for PDE-constrained optimization in inverse problems
    van Leeuwen, T.
    Herrmann, F. J.
    INVERSE PROBLEMS, 2016, 32 (01)
  • [4] A radial basis function method for solving PDE-constrained optimization problems
    John W. Pearson
    Numerical Algorithms, 2013, 64 : 481 - 506
  • [5] A radial basis function method for solving PDE-constrained optimization problems
    Pearson, John W.
    NUMERICAL ALGORITHMS, 2013, 64 (03) : 481 - 506
  • [6] OPTIMAL SOLVERS FOR PDE-CONSTRAINED OPTIMIZATION
    Rees, Tyrone
    Dollar, H. Sue
    Wathen, Andrew J.
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (01) : 271 - 298
  • [7] Domain decomposition in time for PDE-constrained optimization
    Barker, Andrew T.
    Stoll, Martin
    COMPUTER PHYSICS COMMUNICATIONS, 2015, 197 : 136 - 143
  • [8] PDE-constrained optimization with error estimation and control
    Hicken, J. E.
    Alonso, J. J.
    JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 263 : 136 - 150
  • [9] PDE-constrained optimization in medical image analysis
    Andreas Mang
    Amir Gholami
    Christos Davatzikos
    George Biros
    Optimization and Engineering, 2018, 19 : 765 - 812
  • [10] Deep mixed residual method for solving PDE-constrained optimization problems
    Yong, Jinjun
    Luo, Xianbing
    Sun, Shuyu
    Ye, Changlun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 176 : 510 - 524
12345