CONSTRUCTION OF A FINITE ELEMENT BASIS OF THE FIRST DE RHAM COHOMOLOGY GROUP AND NUMERICAL SOLUTION OF 3D MAGNETOSTATIC PROBLEMS

CONSTRUCTION OF A FINITE ELEMENT BASIS OF THE FIRST DE RHAM COHOMOLOGY GROUP AND NUMERICAL SOLUTION OF 3D MAGNETOSTATIC PROBLEMS

We devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic problems. In particular, we construct a finite element basis of the first de Rham cohomology group of the computational domain. The proposed method w...

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Veröffentlicht in:SIAM journal on numerical analysis 2013-01, Vol.51 (4), p.2380-2402
Hauptverfasser: RODRÍGUEZ, ANA ALONSO, BERTOLAZZI, ENRICO, GHILONI, RICCARDO, VALLI, ALBERTO
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Approximation
Construction
Curl
Cutting
Degrees of freedom
Finite element method
Linear systems
Magnetic fields
Magnetism
Magnetostatic fields
Mathematical analysis
Mathematical models
Mathematical problems
Scalars
Three dimensional
Vertices
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Zusammenfassung:We devise an efficient algorithm for the finite element approximation of harmonic fields and the numerical solution of three-dimensional magnetostatic problems. In particular, we construct a finite element basis of the first de Rham cohomology group of the computational domain. The proposed method works for general topological configurations and does not need the determination of "cutting" surfaces.
ISSN:0036-1429
1095-7170
DOI:10.1137/120890648