A hybrid IGAFEM/IGABEM formulation for two-dimensional stationary magnetic and magneto-mechanical field problems

Isogeometric Analysis (IGA) can bridge the gap between geometrical and numerical modelling. To this end, the same functions used in Computer Aided Design are applied to represent geometry and approximate field variables in the numerical model. The concept has already been implemented to solve field problems using Finite Element (FEM) and Boundary Element Methods (BEM) but coupling of both methods has not been applied. In the current work an isogeometric FEM/BEM coupling is proposed and applied to two-dimensional stationary magnetic field problems. While FEM is used to model magnetisable bodies allowing for heterogeneous structures and non-linear constitutive behaviour, the BEM domain accounts for the surrounding free space. Both methods are coupled on the surface of the magnetisable body. Due to this hybrid IGAFEM/-BEM approach, no meshing of free space is necessary and truncation errors are avoided for problems to be solved on open, infinite or semi-infinite domains. Once the solution for the magnetic problem is obtained using the hybrid method, IGAFEM is used to solve a magneto-mechanical field problem with one-sided coupling in a subdomain of the magnetic problem. This one-sided coupling is realised by a magnetic stress tensor computed from the solution of the stationary magnetic field problem. From the comparison of error norms and convergence rates for NURBS and discretisations based on Lagrangian polynomials, smaller errors and similar convergence rates are found for the proposed method for the same polynomial order of the basis functions and a comparable mesh size.