A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs

Yoongu Hwang, Jangwoon Lee, Jeehyun Lee, Myoungho Yoon

Research output: Contribution to journalArticle

Abstract

In this study, we apply a domain decomposition algorithm based on optimization technique to optimal control problems governed by an elliptic partial differential equation with random inputs. The domain decomposition is implemented by introducing an auxiliary optimal control problem, which results in a multi-objective optimization problem. We prove the existence of a solution to the resulting optimization problem as well as the convergence to the optimal solution of original control problem. Solutions of the domain decomposition problem are determined from an optimality system and error estimates for finite element approximations are analyzed. Finally, some numerical experiments are provided to confirm theoretical results.

Original languageEnglish
Article number124674
JournalApplied Mathematics and Computation
Volume364
DOIs
Publication statusPublished - 2020 Jan 1

Fingerprint

Elliptic PDE
Decomposition Algorithm
Domain Decomposition
Optimal Control Problem
Decomposition
Optimality System
Elliptic Partial Differential Equations
Multiobjective Optimization Problems
Multiobjective optimization
Finite Element Approximation
Optimization Techniques
Partial differential equations
Error Estimates
Control Problem
Optimal Solution
Numerical Experiment
Optimization Problem
Experiments

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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A domain decomposition algorithm for optimal control problems governed by elliptic PDEs with random inputs. / Hwang, Yoongu; Lee, Jangwoon; Lee, Jeehyun; Yoon, Myoungho.

In: Applied Mathematics and Computation, Vol. 364, 124674, 01.01.2020.

Research output: Contribution to journalArticle

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