In this work we propose a hybrid SBFEM-FEM approach for the efficient calculation of magnetic stray fields in unbounded domains. In magnetostatic boundary value problems, the interaction between the magnetic solid, externally applied magnetic fields and the surrounding exterior domain is of crucial importance. This interaction generates the magnetic stray field, which diminishes in intensity with increasing distance to the solid. For this reason, the overall infinite domain is simulated using a hybrid formulation of the scaled boundary finite element method (SBFEM) and the finite element method. To this end, the entire domain is divided into a finite and an infinite sub-region, referred to as the interior and the exterior domain. While the interior domain is modeled using finite elements, the exterior domain is reduced onto the boundary of the interior domain by using the SBFEM. The latter provides a semi-analytical solution of the considered magnetostatic problem in an unbounded domain, where the externally applied magnetic fields are taken into account. The advantage of this method is the rigorous representation of the surrounding exterior domain without an explicit discretization. Compared to completely discretized systems, significantly better results can be obtained with smaller systems of equations.

在这项工作中，我们提出了一种混合 SBFEM-FEM 方法，用于有效计算无界域中的杂散磁场。在静磁边值问题中，磁性固体、外加磁场和周围外域之间的相互作用至关重要。这种相互作用会产生杂散磁场，其强度随着与固体距离的增加而减小。因此，使用比例边界有限元方法的混合公式模拟整个无限域（SBFEM）和有限元法。为此，将整个域划分为有限和无限子区域，分别称为内部域和外部域。虽然内部域使用有限元建模，但外部域通过使用 SBFEM 减少到内部域的边界。后者在无界域中提供了所考虑的静磁问题的半解析解，其中考虑了外部施加的磁场。这种方法的优点是周围外部域的严格表示，无需显式离散化。与完全离散的系统相比，使用较小的方程组可以获得明显更好的结果。