A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO
Abstract
In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.
- Authors:
-
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1776612
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Science
- Additional Journal Information:
- Journal Volume: 47; Journal ID: ISSN 1877-7503
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; PDE-constrained optimization; PETSc; TAO; adjoint; spectral element method
Citation Formats
Marin, Oana, Constantinescu, Emil, and Smith, Barry. A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO. United States: N. p., 2020.
Web. doi:10.1016/j.jocs.2020.101207.
Marin, Oana, Constantinescu, Emil, & Smith, Barry. A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO. United States. https://doi.org/10.1016/j.jocs.2020.101207
Marin, Oana, Constantinescu, Emil, and Smith, Barry. Fri .
"A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO". United States. https://doi.org/10.1016/j.jocs.2020.101207. https://www.osti.gov/servlets/purl/1776612.
@article{osti_1776612,
title = {A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO},
author = {Marin, Oana and Constantinescu, Emil and Smith, Barry},
abstractNote = {In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.},
doi = {10.1016/j.jocs.2020.101207},
journal = {Journal of Computational Science},
number = ,
volume = 47,
place = {United States},
year = {Fri Sep 11 00:00:00 EDT 2020},
month = {Fri Sep 11 00:00:00 EDT 2020}
}
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