Optimization under adaptive error control for finite element based simulations

Authors:
Bart G. Bloemen Waanders;Brian R. Carnes
Affiliations:
Sandia National Laboratories, Albuquerque, USA 87185;Sandia National Laboratories, Albuquerque, USA 87185
Venue:
Computational Mechanics
Year:
2011

Citing 7
Cited 0

Design patterns: elements of reusable object-oriented software

Design patterns: elements of reusable object-oriented software
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept

SIAM Journal on Control and Optimization
Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver

SIAM Journal on Scientific Computing
Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part II: The Lagrange--Newton Solver and Its Application to Optimal Control of Steady Viscous Flows

SIAM Journal on Scientific Computing
DYNAMIC DATA-DRIVEN INVERSION FOR TERASCALE SIMULATIONS: REAL-TIME IDENTIFICATION OF AIRBORNE CONTAMINANTS

SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Function, Gradient, and Hessian Recovery Using Quadratic Edge-Bump Functions

SIAM Journal on Numerical Analysis
A Framework for the Adaptive Finite Element Solution of Large-Scale Inverse Problems

SIAM Journal on Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Optimization problems constrained by complex dynamics can lead to computationally challenging problems especially when high accuracy and efficiency are required. We present an approach to adaptively control numerical errors in optimization problems approximated using the finite element method. The discrete adjoint equation serves as a key tool to efficiently compute both parameter sensitivities and goal-oriented error estimates at the same discretized levels. By using a recovery method for the error estimators, we avoid expensive higher order adjoint calculations. We nest the adaptivity of the mesh within the optimization algorithm, which is responsible for converging both the state and optimization algorithms and thereby allowing the reuse of state, parameters, and reduced Hessian in subsequent optimization iterations. Our approach is demonstrated on a parameter estimation problem for contamination transport in a contact tank reactor. Significant efficiency and accuracy improvements are realized in comparison to uniform grid refinement strategies and black-box optimization methods. A flexible and maintainable software interface was developed to provide access between the underlying linear algebra of a production simulator and advanced numerical algorithms such as optimization and error estimation.