A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics

Popis výsledku v původním jazyce

The paper deals with a fast computational method for discretized optimal shape design problems governed by 2--dimensional magnetostatics. We discretize the underlying state problem using linear Lagrange triangular finite elements and in the optimizationwe eliminate the state problem for each shape design. The shape to be optimized is the interface between the ferromagnetic and air domain. The novelty of our approach is that shape perturbations do not affect grid nodal displacements, which is the case of the traditional moving--grid approach, but they are rather mapped to the coefficient function of the underlying magnetostatic operator. The advantage is that there is no additional restriction for the shape perturbations on fine discretizations. However, this approach often leads to a decay of the finite element convergence rate, which we discuss. The computational efficiency of our method relies on an algebraic multigrid solver for the state problem, which is also described in the pap

Název v anglickém jazyce

A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics

Popis výsledku anglicky

The paper deals with a fast computational method for discretized optimal shape design problems governed by 2--dimensional magnetostatics. We discretize the underlying state problem using linear Lagrange triangular finite elements and in the optimizationwe eliminate the state problem for each shape design. The shape to be optimized is the interface between the ferromagnetic and air domain. The novelty of our approach is that shape perturbations do not affect grid nodal displacements, which is the case of the traditional moving--grid approach, but they are rather mapped to the coefficient function of the underlying magnetostatic operator. The advantage is that there is no additional restriction for the shape perturbations on fine discretizations. However, this approach often leads to a decay of the finite element convergence rate, which we discuss. The computational efficiency of our method relies on an algebraic multigrid solver for the state problem, which is also described in the pap

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Lecture Notes in Computer Science-Computational Science

ISBN

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ISSN

0302-9743

e-ISSN

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Počet stran výsledku

9

Strana od-do

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Název nakladatele

Springer-Verlag Berlin Heidelberg

Místo vydání

Berlin Heidelberg

Místo konání akce

Sozopol, Bulharsko

Datum konání akce

5. 7. 2007

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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