Figure 1 - Anisotropic magnetoelectric sphere with a scalar coupling coefficient in an external homogeneous electric field E_0 in the z-direction. (a) Reduced electric field 〖E-E〗_0 outside and inside the sphere (red cones) and the distribution of the electric surface charge density η_e on the sphere surface in the plane y=0. (b) Distribution of the normalized defects in the plane 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 shows the position of the maximum of η_e.
Figure 1 - Anisotropic magnetoelectric sphere with a scalar coupling coefficient in an external homogeneous electric field E_0 in the z-direction. (a) Reduced electric field 〖E-E〗_0 outside and inside the sphere (red cones) and the distribution of the electric surface charge density η_e on the sphere surface in the plane y=0. (b) Distribution of the normalized defects in the plane 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 shows the position of the maximum of η_e.

Magnetoelectric materials allow magnetic properties to be specifically influenced by electric fields and vice versa. This extraordinary coupling opens up a wide range of applications for these materials. They have already been investigated for wireless neural stimulation, cancer therapies, wireless energy transmission, implantable bioelectronics and numerous other applications. 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. For realistic, arbitrarily shaped structures, however, the finite element method is usually used. This requires the discretization of the entire volume of the material and is therefore associated with high computational costs. A significant reduction in computational costs can be achieved using the boundary element method, as only the surfaces need to be discretized.

For anisotropic magnetoelectric materials, however, no established standard boundary element formulation exists so far, since 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 a transformation into an isotropic equivalent problem. Verification using a magnetoelectric anisotropic sphere shows a very high accuracy, with a root mean square error of less than 0.1 % for the electric field and less than 0.2 % for the magnetic field.

 

B. Petković, M. Ziolkowski, J. Haueisen and Hannes Toepfer Boundary Element Modeling of Magnetoelectric Anisotropic Materials IEEE Transactions on Magnetics, vol. 62, no. 1, pp. 1-9, January 2026, Art no. 7200209.

doi: 10.1109/TMAG.2025.3639930

 

Contact person: Dr.-Ing. Bojana Petkovic

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