Geometric T–Ω approach to solve eddy currents coupled to electric circuits

This paper describes a systematic geometric approach to solve magneto-quasi-static coupled field–circuit problems. The field problem analysis is based on formulating the boundary value problem with an electric vector potential and a scalar magnetic potential. The field–circuit coupling and the definition of potentials are formally examined within the framework of homology theory. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  T. Tarhasaari,et al.  State variables for coupled circuit-field problems , 2004, IEEE Transactions on Magnetics.

[2]  A. Bossavit A rationale for 'edge-elements' in 3-D fields computations , 1988 .

[3]  Lauri Kettunen,et al.  Discrete spaces for div and curl-free fields , 1998 .

[4]  H. Flanders Differential Forms with Applications to the Physical Sciences , 1964 .

[5]  Norman Balabanian,et al.  Electrical Network Theory , 1969 .

[6]  L. Kettunen,et al.  Geometric Interpretation of Discrete Approaches to Solving Magnetostatics , 2003 .

[7]  P. Bamberg,et al.  A course in mathematics for students of physics , 1990 .

[8]  Paul W. Gross,et al.  Electromagnetic Theory and Computation: A Topological Approach , 2004 .

[9]  A. Bossavit On the geometry of electromagnetism. : (2):Geometrical objects , 1998 .

[10]  L. Kettunen,et al.  Geometric interpretation of discrete approaches to solving magnetostatic problems , 2004, IEEE Transactions on Magnetics.

[11]  Y. Wong,et al.  Differentiable Manifolds , 2009 .

[12]  Zhuoxiang Ren,et al.  T-/spl Omega/ formulation for eddy-current problems in multiply connected regions , 2002 .

[13]  T. Tarhasaari,et al.  Some realizations of a discrete Hodge operator: a reinterpretation of finite element techniques [for EM field analysis] , 1999 .

[14]  A. Bossavit How weak is the "weak solution" in finite element methods? , 1998 .

[15]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[16]  Enzo Tonti,et al.  Finite formulation of electromagnetic field , 2002 .

[17]  R. Ho Algebraic Topology , 2022 .

[18]  A. Bossavit On the geometry of electromagnetism , 1998 .

[19]  Saku Suuriniemi,et al.  Homological computations in electromagnetic modeling , 2004 .

[20]  E. Tonti Finite Formulation of the Electromagnetic Field , 2001 .

[21]  Kay Hameyer,et al.  An algorithm to construct the discrete cohomology basis functions required for magnetic scalar potential formulations without cuts , 2002 .

[22]  Christophe Geuzaine,et al.  GetDP: a general environment for the treatment of discrete problems , 1997 .

[23]  Lauri Kettunen,et al.  Formulation of the eddy current problem in multiply connected regions in terms of h , 1998 .

[24]  A. Bossavit Most general "non-local" boundary conditions for the Maxwell equation in a bounded region , 2000 .