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Main Title: Encoding electromagnetic transformation laws for dimensional reduction
Author(s): Lehmann, Marcus Christian
Hadžiefendić, Mirsad
Piwonski, Albert
Schuhmann, Rolf
Type: Article
Abstract: Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be justified that the derivative in symmetry direction is constant or even vanishing. A generalized notion of symmetry can be defined with different directions at every point in space, as long as it is possible to exhibit unidirectional symmetry in some coordinate representation. This can be achieved, for example, when the symmetry direction is given by the direct construction out of a unidirectional symmetry via a coordinate transformation which poses a demand on the boundary value problem. Coordinate independent formulations of boundary value problems do exist but turning that theory into practice demands a pedantic process of backtranslation to the computational notions. This becomes even more challenging when multiple chained transformations are necessary for propagating a symmetry. We try to fill this gap and present the more general, isolated problems of that translation. Within this contribution, the partial derivative and the corresponding chain rule for multivariate calculus are investigated with respect to their encodability in computational terms. We target the layer above univariate calculus, but below tensor calculus.
Subject(s): computational electromagnetism
coordinate transformations
Issue Date: 25-May-2020
Date Available: 8-Dec-2020
Language Code: en
DDC Class: 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Sponsor/Funder: TU Berlin, Open-Access-Mittel – 2020
Journal Title: International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Publisher: Wiley
Volume: 33
Issue: 5
Article Number: e2747
Publisher DOI: 10.1002/jnm.2747
EISSN: 1099-1204
ISSN: 0894-3370
TU Affiliation(s): Fak. 4 Elektrotechnik und Informatik » Inst. Hochfrequenz- und Halbleiter-Systemtechnologien » FG Theoretische Elektrotechnik
Appears in Collections:Technische Universität Berlin » Publications

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