Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - EJOUR
AU - Lehmann, Marcus Christian
AU - Hadžiefendić, Mirsad
AU - Piwonski, Albert
AU - Schuhmann, Rolf
PY - 2020
TI - Encoding electromagnetic transformation laws for dimensional reduction
T2 - International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
DO - 10.1002/jnm.2747
UR - https://doi.org/10.1002/jnm.2747
VL - 33
IS - 5
SP - e2747
N1 - Available Open Access publishedVersion at https://depositonce.tu-berlin.de/handle/11303/12134
LA - en
AB - 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.
KW - computational electromagnetism
KW - coordinate transformations
KW - lambda‐Calculus
ER -