Mesh Deformation Based on Radial Basis Function Interpolation Applied to Low-Frequency Electromagnetic Problem

In order to take into account a modification of the geometry during an optimization process or due to a physical phenomenon, a deformation of the elements of the spatial discretization is preferable to conserve a conformal mesh and to apply the finite element (FE) method. To perform the displacement of nodes, an interpolation method can be investigated in this context. In this paper, the radial basis function (RBF) interpolation method is applied for low-frequency electromagnetic problems solved by the FE method. A 2-D magnetostatic example is considered to study the influence of the parameters of the RBF interpolation. To test the extension in 3-D, a nondestructive testing problem is treated, where the shape of the crack is modified by applying the proposed method.