Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency

Abstract : The classical energy minimization principles of Dirichlet and Thompson are extended as minimization principles to acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency. This is done by building upon ideas of Cherkaev and Gibiansky, who derived minimization variational principles for quasistatics. In the absence of free current the primary electromagnetic minimization variational principles have a minimum which is the time-averaged electrical power dissipated in the body. The variational principles provide constraints on the boundary values of the fields when the moduli are known. Conversely, when the boundary values of the fields have been measured, then they provide information about the values of the moduli within the body. This should have application to electromagnetic tomography. We also derive saddle point variational principles which correspond to variational principles of Gurtin, Willis, and Borcea.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00523225
Contributor : Pierre Seppecher <>
Submitted on : Monday, October 4, 2010 - 3:26:27 PM
Last modification on : Tuesday, June 19, 2018 - 4:02:01 PM
Long-term archiving on : Friday, December 2, 2016 - 10:16:16 AM

File

miltonseppecherbouchittA_1.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00523225, version 1

Collections

Citation

Graeme W. Milton, Pierre Seppecher, Guy Bouchitté. Minimization variational principles for acoustics, elastodynamics, and electromagnetism in lossy inhomogeneous bodies at fixed frequency. 2010. ⟨hal-00523225⟩

Share

Metrics

Record views

298

Files downloads

144