On the Optimal Control of a Linear Peridynamics Model

被引：1
作者：
Mengesha, Tadele [1 ]
Salgado, Abner J. [1 ]
Siktar, Joshua M. [1 ]
机构：
[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2023年 / 88卷 / 03期
基金：
美国国家科学基金会;
关键词：
Peridynamics; Optimal control; Asymptotic compatibility; Integral equations; Non-local systems; Bond-based model; ASYMPTOTICALLY COMPATIBLE SCHEMES; FRACTIONAL LAPLACIAN; FRACTURE; LIMIT; CONVERGENCE; REGULARITY; EQUATION;
D O I：
10.1007/s00245-023-10045-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a non-local optimal control problem involving a linear, bond-based peridy-namics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter d, which controls the degree of nonlocality, approaches zero. We then study a finite element-based discretization of this problem, its convergence, and the so-called asymptotic compatibility as the discretization parameter h and the horizon parameter d tend to zero simultaneously.
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页数：43
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