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Title: Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report)

Abstract

The objectives of this project are to devise and analyze efficient solvers for several classes of PDE- constrained optimization problems. The project was initially focused on, but not restricted to time- dependent PDE-constraints such as parabolic equations, time-dependent fluid flows (Navier-Stokes equations), hyperbolic equations (Burgers equation, shallow water equations). Other constraints considered are PDEs with stochastic coefficients. Additional elements of interest are the handling of problems with control and/or state inequality constraints or non-differentiable regularization terms, and boundary controls. A direction of work not initially listed among the goals, which was triggered by conversations with DOE scientists from the Sandia National Labs, is to develop efficient solvers for optimization- based domain-decomposition PDE-solvers. Also targeted in the project are a number of technical issues necessary for facilitating the integration of the methods resulted from this project with existing high-performance packages developed at DOE national labs; this integration is expected to further enable the scientific community to use the novel methods. An example of such a task is the need to develop algebraic multigrid (AMG) versions of the algorithms. A list of accomplishments in several areas is detailed as well as a list of publications.

Authors:
 [1]
  1. Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
Publication Date:
Research Org.:
Univ. of Maryland Baltimore County (UMBC), Baltimore, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1494701
Report Number(s):
DOE-UMBC-DE-SC0005455
DOE Contract Number:  
SC0005455
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; PDE-constrained optimization; multigrid

Citation Formats

Draganescu, Andrei. Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report). United States: N. p., 2019. Web. doi:10.2172/1494701.
Draganescu, Andrei. Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report). United States. https://doi.org/10.2172/1494701
Draganescu, Andrei. 2019. "Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report)". United States. https://doi.org/10.2172/1494701. https://www.osti.gov/servlets/purl/1494701.
@article{osti_1494701,
title = {Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report)},
author = {Draganescu, Andrei},
abstractNote = {The objectives of this project are to devise and analyze efficient solvers for several classes of PDE- constrained optimization problems. The project was initially focused on, but not restricted to time- dependent PDE-constraints such as parabolic equations, time-dependent fluid flows (Navier-Stokes equations), hyperbolic equations (Burgers equation, shallow water equations). Other constraints considered are PDEs with stochastic coefficients. Additional elements of interest are the handling of problems with control and/or state inequality constraints or non-differentiable regularization terms, and boundary controls. A direction of work not initially listed among the goals, which was triggered by conversations with DOE scientists from the Sandia National Labs, is to develop efficient solvers for optimization- based domain-decomposition PDE-solvers. Also targeted in the project are a number of technical issues necessary for facilitating the integration of the methods resulted from this project with existing high-performance packages developed at DOE national labs; this integration is expected to further enable the scientific community to use the novel methods. An example of such a task is the need to develop algebraic multigrid (AMG) versions of the algorithms. A list of accomplishments in several areas is detailed as well as a list of publications.},
doi = {10.2172/1494701},
url = {https://www.osti.gov/biblio/1494701}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Feb 14 00:00:00 EST 2019},
month = {Thu Feb 14 00:00:00 EST 2019}
}