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

页码：1896 / 1917

页数：22

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