000 05027nam a22004935i 4500
001 978-94-007-0202-8
003 DE-He213
005 20140220082527.0
007 cr nn 008mamaa
008 130930s2014 ne | s |||| 0|eng d
020 _a9789400702028
_9978-94-007-0202-8
024 7 _a10.1007/978-94-007-0202-8
_2doi
050 4 _aQA71-90
072 7 _aPDE
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aMAT003000
_2bisacsh
082 0 4 _a004
_223
100 1 _aTouzani, Rachid.
_eauthor.
245 1 0 _aMathematical Models for Eddy Currents and Magnetostatics
_h[electronic resource] :
_bWith Selected Applications /
_cby Rachid Touzani, Jacques Rappaz.
264 1 _aDordrecht :
_bSpringer Netherlands :
_bImprint: Springer,
_c2014.
300 _aXII, 305 p. 42 illus., 31 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aScientific Computation,
_x1434-8322
505 0 _aPart I Eddy Current Models -- Mathematical framework -- Introduction -- Preliminaries.- The Three-Dimensional Case -- The Two-Dimensional Case -- Maxwell and eddy current equations -- Introduction -- Maxwell equations -- Low frequency approximation -- Static cases.- Time{Harmonic Regime -- Eddy Current Equations -- Two-dimensional models.- Introduction -- A solenoidal two-dimensional model -- A transversal model -- Three-dimensional models.-  A current density formulation -- A magnetic field formulation -- An electric field model -- Axisymmetric models -- Axisymmetric setting -- A magnetic field model -- A scalar potential model -- Eddy current models with thin inductors -- The two-dimensional solenoidal model -- The two-dimensional transversal model -- Three-dimensional models -- Numerical Methods -- Introduction and main notations -- Standard (H1) finite element method -- A finite element method for the 2-D solenoidal model -- Finite elements for the axisymmetric model.-  Finite elements in H(curl){spaces.- Finite elements in H(div){spaces -- The boundary element method for boundary integral equations -- Approximation of a domain integral equation -- Coupled finite element/boundary element methods -- Part II Selected Applications -- Induction Heating Processes.-  A mathematical model.- Bibliographical comments -- A 2-D stationary problem -- A 2-D time dependent problem.- Numerical experiments.-  An optimal control problem -- Magnetohydrodynamics and Magnetic Shaping -- Incompressible Magnetohydrodynamics.-  Eddy current free boundary problems.- An Electromagnetic Casting problem -- Inductively coupled plasma torches.-  The model.-  Numerical approximation -- A numerical simulation.- Ferromagnetic Shielding.-  Mathematical analysis.-  An iterative procedure.- Solution of the linear problem by a domain decomposition method.-  An iterative procedure for the discrete nonlinear problem.-  Numerical results.- The electrolytic process for aluminium production -- Introduction.- The model -- Numerical approximation -- Numerical results -- Mathematical Symbols -- References -- Index.
520 _aThis monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.
650 0 _aMathematics.
650 0 _aComputer science.
650 0 _aEngineering mathematics.
650 1 4 _aMathematics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
700 1 _aRappaz, Jacques.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789400702011
830 0 _aScientific Computation,
_x1434-8322
856 4 0 _uhttp://dx.doi.org/10.1007/978-94-007-0202-8
912 _aZDB-2-PHA
999 _c93831
_d93831