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The purpose of this paper is to present a hybrid numerical simulation approach for the calculation of potential and electric field distribution considering charge and dielectric constant.

Each numerical method has its own advantages and disadvantages. The idea is to overcome the disadvantages of the corresponding numerical method by coupling with other numerical methods. An augmented finite element method (FEM), linear FEM and boundary element method are used with an efficient coupling.

The simulation model of microstructured devices is not so simple. During the simulation various types of problems will occur. It is found that by using several numerical methods these problems can be overcome and the calculation can be performed efficiently.

The present approach can be applied in 2D cases. But, in 3D cases the calculation of augmented FEM in a spherical coordinate becomes quite elaborate.

The proposed hybrid numerical simulation approach can be applied for the simulation of the electrostatic force microscope (EFM) which is a very high‐resolution measuring tool in nanotechnology. This approach can be applied also to other micro‐electro‐mechanical systems.

Since the scanning process of the EFM is dynamic, it requires the updating of the FEM mesh in each calculation time step. In the present paper, the mesh updating is achieved by an arbitrary Lagrangian‐Eulerian (ALE) method. The proposed numerical approach can be applied for the simulation of the EFM including this remeshing algorithm ALE.

The purpose of this paper is to introduce a method which allows the calculation of the interactions of tip and sample of a magnetic force microscope as a first step to increase the accuracy of this technique.

The emerging magnetic interactions between the cantilever tip and an arbitrary magnetized sample can be evaluated by the use of several numerical methods. For modelling this magnetically and mechanically coupled multiscale problem the finite element method is implemented.

The evaluated magnetic fields interact in such a manner that a constructive overlap at the tip apex occurs. This leads to attractive forces acting on the cantilever.

In order to include the magneto‐mechanical coupling, the implementation of a detailed force calculation is necessary. Furthermore, a hysteresis model is not yet considered.

Magnetic force microscopy is a very sensitive technique. For instance, ideally the end of the tip consists of only one atom, but this is not realizable. Measurement errors cannot be avoided. This approach is the first step in developing an opportunity to soften them.

One opportunity to verify real‐time magnetic force microscope measurements is the comparison with theoretical considerations and calculations of the occurring magnetic distribution by using this technique. For this reason this paper deals with a new micromagnetic model to simulate the interactions between tip and sample of a scanning process of a magnetic force microscope.