Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal-dual interior point method

Autor(es)

Nigro, P. S. B. ^{[1, 2]} ; Simoes, T. ^[1] ; Pimenta, P. M. ^[3] ; Schroeder, J. ^[2]

Afiliação do(s) autor(es)

^[1] VirtualPYXIS Optimizat, Sao Caetano do Sul - Brazil

^[2] Univ Duisburg Essen, Inst Mech, Univ Str 15, D-45141 Essen - Germany

^[3] Univ Sao Paulo, Dept Struct & Geotech Engn, Polytech Sch, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 120, n. 12 AUG 2019.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 16/03528-4 - Redução de ordem de modelos aplicada à otimização topológica
• Beneficiário: Paulo Salvador Britto Nigro
• Modalidade de apoio: Bolsas no Brasil - Programa Capacitação - Treinamento Técnico
• Processo FAPESP: 16/04460-4 - Redução de ordem de modelos aplicada à otimização topológica
• Beneficiário: Eduardo Tenório Simões
• Modalidade de apoio: Bolsas no Brasil - Programa Capacitação - Treinamento Técnico