On the stability of harmonic mortar methods with application to electric machines

Harmonic stator-rotor coupling offers a promising approach for the interconnection of rotating subsystems in the simulation of electric machines. This paper studies the stability of discretization schemes based on harmonic coupling in the framework of mortar methods for Poisson-like problems. A general criterion is derived that allows to ensure the relevant inf-sup stability condition for a variety of specific discretization approaches, including finite-element methods and isogeometric analysis with harmonic mortar coupling. The validity and sharpness of the theoretical results is demonstrated by numerical tests.

[1]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[2]  P. Clément.  Approximation by finite element functions using local regularization , 1975 .

[3]  Peter Hansbo,et al.  A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes , 2005, Numerische Mathematik.

[4]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[5]  Giancarlo Sangalli,et al.  On Quasi-Interpolation Operators in Spline Spaces , 2015 .

[6]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[7]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[8]  H. De Gersem,et al.  Harmonic weighting functions at the sliding interface of a finite-element machine model incorporating angular displacement , 2004, IEEE Transactions on Magnetics.

[9]  Zeger Bontinck,et al.  Isogeometric analysis and harmonic stator–rotor coupling for simulating electric machines , 2017, Computer Methods in Applied Mechanics and Engineering.

[10]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[11]  Wolfgang Dahmen,et al.  A Multigrid Algorithm for the Mortar Finite Element Method , 1999, SIAM J. Numer. Anal..

[12]  P. Raviart,et al.  Primal hybrid finite element methods for 2nd order elliptic equations , 1977 .

[13]  Christophe Geuzaine,et al.  A general method for the frequency domain FE modeling of rotating electromagnetic devices , 2003 .

[14]  Barbara Wohlmuth,et al.  Isogeometric mortar methods , 2014, 1407.8313.

[15]  Kay Hameyer,et al.  A Variational Formulation for Nonconforming Sliding Interfaces in Finite Element Analysis of Electric Machines , 2010, IEEE Transactions on Magnetics.

[16]  Alessandro Reali,et al.  GeoPDEs: A research tool for Isogeometric Analysis of PDEs , 2011, Adv. Eng. Softw..

[17]  Barbara I. Wohlmuth,et al.  A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier , 2000, SIAM J. Numer. Anal..

[18]  L. R. Scott,et al.  Finite element interpolation of nonsmooth functions satisfying boundary conditions , 1990 .