A Novel h-φ Approach for Solving Eddy-Current Problems in Multiply Connected Regions

• Published in: IEEE access 2020, Vol.8, p.170659-170671
• Main Authors: Moro, Federico, Smajic, Jasmin, Codecasa, Lorenzo
• Format: Article
• Language: English
• Subjects: Basis functions; cell method; Coils; Computing time; cut; Eddy currents; Electric potential; Faces; Finite element analysis; Finite element method; Gaging; Generators; Iterative methods; Magnetic domains; Magnetic vector potentials; Mathematical analysis; Matrix methods; multiply connected; Software; Topology
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2020.3025291

A novel \mathbf {h} - \boldsymbol {\varphi } approach for solving 3-D time-harmonic eddy current problems is presented. It makes it possible to limit the number of degrees of freedom required for the discretization such as the \mathbf {T} - \Omega method, while overcoming topological issues related to it when multiply connected domains are considered. Global basis functions, needed for representing magnetic field in the insulating region, are obtained by a fast iterative solver. The computation of thick cuts by high-complexity computational topology tools, typically required by the \mathbf {T} - \Omega method, is thus avoided. The final matrix system turns out to be symmetric and full-rank unlike the more classical \mathbf {A} - \mathbf {A} method, which requires gauging of magnetic vector potential to ensure uniqueness. Numerical tests show that the proposed method is accurate and the field problem solution is obtained in a reasonable computational time even for 3-D models with millions of mesh elements.