An optimization based domain decomposition method for PDEs with random inputs

Jangwoon Lee, Jeehyun Lee, Yoongu Hwang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

An optimization-based domain decomposition method for stochastic elliptic partial differential equations is presented. The main idea of the method is a constrained optimization problem for which the minimization of an appropriate functional forces the solutions on the two subdomains to agree on the interface; the constraints are the stochastic partial differential equations. The existence of optimal solutions for the stochastic optimal control problem is shown as is the convergence to the exact solution of the given problem. We prove the existence of a Lagrange multiplier and derive an optimality system from which solutions of the domain decomposition problem may be determined. Finite element approximations to the solutions of the optimality system are defined and analyzed with respect to both spatial and random parameter spaces. Then, the results of some numerical experiments are given to confirm theoretical error estimate results.

Original languageEnglish
Pages (from-to)2262-2276
Number of pages15
JournalComputers and Mathematics with Applications
Volume68
Issue number12
DOIs
Publication statusPublished - 2014 Dec 1

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Domain decomposition methods
Optimality System
Stochastic Partial Differential Equations
Domain Decomposition Method
Stochastic Optimal Control
Random Parameters
Partial differential equations
Optimization
Elliptic Partial Differential Equations
Constrained Optimization Problem
Domain Decomposition
Finite Element Approximation
Lagrange multipliers
Parameter Space
Optimal Control Problem
Error Estimates
Optimal Solution
Exact Solution
Numerical Experiment
Constrained optimization

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

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An optimization based domain decomposition method for PDEs with random inputs. / Lee, Jangwoon; Lee, Jeehyun; Hwang, Yoongu.

In: Computers and Mathematics with Applications, Vol. 68, No. 12, 01.12.2014, p. 2262-2276.

Research output: Contribution to journalArticle

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