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Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions

Oleg Burdakov (oleg.burdakov***at***liu.se)
Ivan Kapyrin (ivan.kapyrin***at***gmail.com)
Yuri Vassilevski (yuri.vassilevski***at***gmail.com)

Abstract: We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. It is based on solving a monotonic regression problem with some extra constraints. One of them is a linear equality-type constraint which models the conservativity requirement. The other ones are box-type constraints, and they originate from the discrete maximum principle. The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessed FE solution preserves the accuracy of the discrete FE approximation. We introduce an algorithm for solving the postprocessing problem. It can be viewed as a dual ascent method based on the Lagrangian relaxation of the equality constraint. We justify theoretically its correctness. Its efficiency is demonstrated by the presented results of numerical experiments.

Keywords: Constrained monotonic regression, Large scale quadratic optimization, Lagrangian relaxation, Dual ascent method, Finite element solution, Accuracy analysis

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Technical Report LiTH-MAT-R-2011/08-SE, Department of Mathematics, Linköping University, Sweden, 2011

Download: [PDF]

Entry Submitted: 04/14/2011
Entry Accepted: 04/14/2011
Entry Last Modified: 04/19/2011

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