Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method. (16th August 2019)

• Record Type: Journal Article
• Authors: Nigro, P.S.B.; Simões, E.T.; Pimenta, P.M.; Schröder, J.
• Is Part Of: International journal for numerical methods in engineering. Volume 120:Number 12(2019)
• Page Start: 1310
• Page End: 1348
• Publication Date: 2019-08-16
• Subjects: Galerkin projection -- interior point methods -- model order reduction -- nonlinear optimization with constraint -- Schur complement; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6181
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: It is not new that model order reduction (MOR) methods are employed in almost all fields of engineering to reduce the processing time of complex computational simulations. At the same time, interior point methods (IPMs), a method to deal with inequality constraint problems (which is little explored in engineering), can be applied in many fields such as plasticity theory, contact mechanics, micromechanics, and topology optimization. In this work, a MOR based in Galerkin projection is coupled with the infeasible primal‐dual IPM. Such research concentrates on how to develop a Galerkin projection in one field with the interior point method; the combination of both methods, coupled with Schur complement, permits to solve this MOR similar to problems without constraints, leading to new approaches to adaptive strategies. Moreover, this research develops an analysis of error from the Galerkin projection related to the primal and dual variables. Finally, this work also suggests an adaptive strategy to alternate the Galerkin projection operator, between primal and dual variable, according to the error during the processing of a problem.