Precise and robust magnetic field computations for high-end smart sensor applications
Highly precise magnetic field computations are essential for the design of magnets and coils of high-end smart sensors in the context of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) applications. Here, requirements for numerical magnetic field computations are that the methods are precise and mainly robust in the sense of reliable results. Non-linear magnetic materials, induced eddy currents, and the infinite surrounding air domain must be accurately considered in the numerical model. To this end, a smart combination of the finite element method (FEM) with the boundary element method (BEM) including a powerful post-processing is proposed with a focus on the region of interest (ROI), which contains the studied sample. Separate BEM domains are defined for the infinite surrounding air domain and the ROI. Then, the computational costs are reduced due to the relatively small number of relevant boundary elements of the surface of the ROI and a precise and efficient evaluation of magnetic fields based on a meshfree BEM post-processing in the ROI is possible. As an example, the numerical formulation, the application of the proposed approach, and numerical results are shown for the homogeneous field of a permanent magnet.