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dc.contributor.authorAmstutz, Samuel
dc.contributor.authorDapogny, Charles
dc.contributor.authorFerrer Ferré, Àlex
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.identifier.citationAmstutz, S., Dapogny, C., Ferrer, A. A consistent relaxation of optimal design problems for coupling shape and topological derivatives. "Numerische mathematik", setembre 2018, vol. 140, núm. 1, p. 35-94
dc.description.abstractIn this article, we introduce and analyze a general procedure for approximating a ‘black and white’ shape and topology optimization problem with a density optimization problem, allowing for the presence of ‘grayscale’ regions. Our construction relies on a regularizing operator for smearing the characteristic functions involved in the exact optimization problem, and on an interpolation scheme, which endows the intermediate density regions with fictitious material properties. Under mild hypotheses on the smoothing operator and on the interpolation scheme, we prove that the features of the approximate density optimization problem (material properties, objective function, etc.) converge to their exact counterparts as the smoothing parameter vanishes. In particular, the gradient of the approximate objective functional with respect to the density function converges to either the shape or the topological derivative of the exact objective. These results shed new light on the connections between these two different notions of sensitivities for functions of the domain, and they give rise to different numerical algorithms which are illustrated by several experiments
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia
dc.subject.lcshStructural optimization -- Mathematics
dc.subject.lcshMultiscale modeling--Computer simulation
dc.subject.otherLevel set method
dc.subject.otherMaterial interpolation
dc.subject.otherShape derivative
dc.subject.otherOptimal design
dc.subject.othertopological derivative
dc.titleA consistent relaxation of optimal design problems for coupling shape and topological derivatives
dc.subject.lemacOptimització d'estructures
dc.subject.lemacModelització multiescala
dc.contributor.groupUniversitat Politècnica de Catalunya. DECA - Grup de Recerca del Departament d'Enginyeria Civil i Ambiental
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::74 Mechanics of deformable solids::74P Optimization
dc.subject.amsClassificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization::49Q Manifolds
dc.subject.amsClassificació AMS::65 Numerical analysis::65N Partial differential equations, boundary value problems
dc.subject.amsClassificació AMS::49 Calculus of variations and optimal control; optimization::49M Methods of successive approximations
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/320815/EU/Advanced tools for computational design of engineering materials/COMP-DES-MAT
local.citation.authorAmstutz, S.; Dapogny, C.; Ferrer, A.
local.citation.publicationNameNumerische mathematik

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