Quasi-power functionals for potential fields from the Graph- Theoretic Field Model

✍ Scribed by G.J. Savage; H.K. Kesavan

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 558 KB
• Volume: 314
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(82)90077-1

✦ Synopsis

Quasi-power functionals have been traditionally derived through the Method of Weighted Residuals (MWR) and used as the starting formulation for the finite element method. In this paper, we derive similar but more complete functionals for potential fields through a novel approach. We first form discrete quasi-power functions by applying Tellegen's theorem to the Graph-Theoretic Field Model (GTFM) and then obtain the continuous model quasi-power functionals by applying a limiting process to the discrete counterpart. The procedure herein is in marked contrast to the MWR whereby quasi-power functionals are derived by applying mathematical operations to the partial differential system. The procedure can be used with fields with anisotropy, non-linearities and coupled processes, although the example fields used within are linear and isotropic. This paper is a sequel to similar derivations for Green's identities and variational formulations.