Magnetoelectric materials enable the targeted manipulation of magnetic properties by electric fields and vice versa. This extraordinary coupling opens up a wide range of applications for these materials. They have already been tested for wireless neural stimulation, cancer treatments, wireless energy transfer, implantable bioelectronics, and many more. Precise and powerful numerical simulation methods are essential for the development of new components in which magnetic properties and the resulting deformations are to be efficiently controlled by electric fields.
Simple and highly symmetrical geometries can be described analytically. However, for realistic structures of arbitrary shape, the finite element method is generally used. This requires the discretization of the entire volume of the material and is therefore associated with high computational costs. A significant reduction in computing costs can be achieved using the boundary element method, as only the surfaces need to be discretized.
However, there is currently no established standard boundary element formulation for anisotropic magnetoelectric materials, as the corresponding fundamental solutions cannot be represented in closed form. In our work, we therefore present a new approach based on the boundary element source method, which can be used to efficiently model arbitrarily shaped magnetoelectric anisotropic objects in an isotropic background medium. The method works directly with anisotropic material tensors and does not require transformation into an isotropic equivalent problem. Verification using a magnetoelectric anisotropic sphere shows very high numerical accuracy, with a normalized root mean square error of less than 0.1% for the electric field and less than 0.2% for the magnetic field.
Original publication: IEEE Transactions on Magnetics, Boundary Element Modeling of Magnetoelectric Anisotropic Materials
By Bojana Petković, Marek Ziolkowski, Jens Haueisen, and Hannes Toepfer
Figure 1 – Anisotropic magnetoelectric sphere with scalar coupling coefficient in external homogeneous electric field E0 in z-direction. (a) Reduced electric field E-E0 both outside and inside the sphere (red cones), together with the electric charge density distribution ηe on the sphere’s surface, at y=0. (b) Distribution of the normalized errors at y=0. The orange and blue lines represent the field lines of the reduced electric field and the total electric field, respectively. The red marker indicates the location of ηe’s maximum.
