Vector variational problems and applications to optimal design

Pablo Pedregal

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 11, Issue: 3, page 357-381
  • ISSN: 1292-8119

Abstract

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We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical simulation leads to approximated optimal configurations. We include several such simulations in 2d and 3d.

How to cite

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Pedregal, Pablo. "Vector variational problems and applications to optimal design." ESAIM: Control, Optimisation and Calculus of Variations 11.3 (2010): 357-381. <http://eudml.org/doc/90768>.

@article{Pedregal2010,
abstract = { We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical simulation leads to approximated optimal configurations. We include several such simulations in 2d and 3d. },
author = {Pedregal, Pablo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Effective; homogenized or relaxed integrand; gradient Young measures; laminates.; optimal design; Young measures; relaxation},
language = {eng},
month = {3},
number = {3},
pages = {357-381},
publisher = {EDP Sciences},
title = {Vector variational problems and applications to optimal design},
url = {http://eudml.org/doc/90768},
volume = {11},
year = {2010},
}

TY - JOUR
AU - Pedregal, Pablo
TI - Vector variational problems and applications to optimal design
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 11
IS - 3
SP - 357
EP - 381
AB - We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical simulation leads to approximated optimal configurations. We include several such simulations in 2d and 3d.
LA - eng
KW - Effective; homogenized or relaxed integrand; gradient Young measures; laminates.; optimal design; Young measures; relaxation
UR - http://eudml.org/doc/90768
ER -

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