Construction of a finite element basis of the first de Rham cohomology group and numerical solution of 3D magnetostatic problems

Alonso Rodriguez, Ana and Bertolazzi, Enrico and Ghiloni, Riccardo and Valli, Alberto (2012) Construction of a finite element basis of the first de Rham cohomology group and numerical solution of 3D magnetostatic problems. Trento : University of Trento. Department of Mathematics. (Submitted)

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    Abstract

    We devise an efficient algorithm for the finite element construction of discrete harmonic fields and the numerical solution of 3D 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.

    Item Type: Departmental Technical Report
    Department or Research center: Materials Engineering and Industrial Technologies
    Mathematics
    Subjects: Q Science > QA Mathematics > QA063 Problem solving
    Q Science > QA Mathematics > QA374.7 Partial differential equations
    Q Science > QA Mathematics > QA611 Topology
    Uncontrolled Keywords: Edge finite elements, discrete harmonic fields, first de Rham cohomology group, magnetostatics, loop fields, source fields.
    Report Number: UTM 753
    Repository staff approval on: 21 Jun 2012 17:28

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