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| Description
| - 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 optimization we 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 paper. At the end w
- 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 optimization we 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 paper. At the end w (en)
- Tento článek se zabývá rychlou výpočetní metodou pro diskretizované úlohy tvarové optimalizace ve 2-dimenzionální magnetostatice. Stavovou úlohu diskretizujeme lineárními Lagrangeovskými konečnými prvky a v rámci tvarové optimalizace ji eliminujeme pro každý návrh. Optimalizovaný tvar popisuje rozhraní mezi feromagnetikem a vzduchem. Náš přístup je nový v tom, že změna tvaru neovlivňuje posunutí sítě, viz tradiční přístup, ale je mapována na funkci materiálových koeficientů příslušného magnetostatického operátoru. Výhodou je, že odpadá nutnost omezení rozsáhlých perturbací na jemných sítích. Nevýhodou je, že náš přístup snižuje řád konvergence metody konečných prvků. Efektivita výpočtu se opírá o algebraický multigrid, který v článku popisujeme. Na závěr uvádíme numerické výsledky. (cs)
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| Title
| - A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics
- A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics (en)
- A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics (cs)
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| skos:prefLabel
| - A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics
- A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics (en)
- A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics (cs)
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| skos:notation
| - RIV/61989100:27240/08:00018821!RIV09-MSM-27240___
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(1ET400300415), P(GP201/05/P008), Z(MSM6198910027)
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/61989100:27240/08:00018821
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - shape optimization; magnetostatics; algebraic multigrid (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...v/mistoKonaniAkce
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...i/riv/nazevZdroje
| - Lecture Notes in Computer Science-Computational Science
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
| - Lukáš, Dalibor
- Kraus, J. K.
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| http://linked.open...vavai/riv/typAkce
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| http://linked.open.../riv/zahajeniAkce
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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| http://purl.org/ne...btex#hasPublisher
| - Springer-Verlag. (Berlin; Heidelberg)
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| http://localhost/t...ganizacniJednotka
| |
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