Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Holding the Fields Constant: A Shape-Calulus Approach to Electromagnetic Forces

by P. Panchal and R. Hiptmair and S. Kurz

(Report number 2024-19)

Abstract
Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held belief that the virtual work principle entails passively advecting the fields with the virtual displacement when computing deformation-dependent field energies gradients. The adjoint approach to differentiation of functionals under variational constraints provides a mathematical justification for this belief. However, it also shows that passively advecting the actual electromagnetic fields is sufficient only in the case of linear materials. In the general case, also fields arising as solutions of adjoint variational problems have to be taken into account.

Keywords: shape calculus, electromagnetic forces, virtual work principle, adjoint variational problems

@Techreport{PHK24_1101,
  author = {P. Panchal and R. Hiptmair and S. Kurz},
  title = {Holding the Fields Constant: A Shape-Calulus Approach to Electromagnetic Forces},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2024-19},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2024/2024-19.pdf },
  year = {2024}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).