On solution to an optimal shape design problem in 3-dimensional linear magnetostatics

Dalibor Lukáš

Applications of Mathematics (2004)

  • Volume: 49, Issue: 5, page 441-464
  • ISSN: 0862-7940

Abstract

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In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards.

How to cite

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Lukáš, Dalibor. "On solution to an optimal shape design problem in 3-dimensional linear magnetostatics." Applications of Mathematics 49.5 (2004): 441-464. <http://eudml.org/doc/33194>.

@article{Lukáš2004,
abstract = {In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards.},
author = {Lukáš, Dalibor},
journal = {Applications of Mathematics},
keywords = {optimal shape design; finite element method; magnetostatics; magnetooptics; optimal shape design; finite element method; magnetostatics; magnetooptics},
language = {eng},
number = {5},
pages = {441-464},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On solution to an optimal shape design problem in 3-dimensional linear magnetostatics},
url = {http://eudml.org/doc/33194},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Lukáš, Dalibor
TI - On solution to an optimal shape design problem in 3-dimensional linear magnetostatics
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 5
SP - 441
EP - 464
AB - In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization problem and prove the convergence of the approximated solutions. In the end, we solve the problem for the optimal shape of an electromagnet that arises in the research on magnetooptic effects and that was manufactured afterwards.
LA - eng
KW - optimal shape design; finite element method; magnetostatics; magnetooptics; optimal shape design; finite element method; magnetostatics; magnetooptics
UR - http://eudml.org/doc/33194
ER -

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