A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

Marin, Oana; Constantinescu, Emil; Smith, Barry

doi:10.1016/j.jocs.2020.101207

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

Journal Article · Fri Sep 11 00:00:00 EDT 2020 · Journal of Computational Science

DOI:https://doi.org/10.1016/j.jocs.2020.101207· OSTI ID:1776612

Marin, Oana ^[1]; Constantinescu, Emil ^[1]; Smith, Barry ^[1]

Argonne National Lab. (ANL), Lemont, IL (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1776612

Journal Information:: Journal of Computational Science, Journal Name: Journal of Computational Science Vol. 47; ISSN 1877-7503

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

97 MATHEMATICS AND COMPUTING
PDE-constrained optimization
PETSc
TAO
adjoint
spectral element method

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

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References (15)

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