Simulation of singularity in the potential problem with semi-analytical elements

•Two new singular boundary elements are constructed to model the singular flux density filed.•The proposed method can analyze the singular flux density field of any material properties.•The proposed method can obtain more accurate results without much computational cost.•The first three singular coefficients can be determined without post processing. Based on the asymptotic solutions for primer and gradient fields, two novel semi-analytical elements are respectively proposed to evaluate potential and flux density in the 2D domain with singularity. By setting two semi-analytical elements on both sides of the singular point, the physical fields in the vicinity of the singular point can be simulated, while boundary element method is implemented for the rest part. Due to asymptotic solutions, the first three singular coefficients are set as the unknowns. The semi-analytical elements are firstly applied on the isotropic material. Regarding to the orthotropic and anisotropic materials, the coordinate system transformation method is applied to transform the governing equation into the isotropic format. Then, semi-analytical elements can be set in the new calculation domain to evaluate potential and flux density. At last, by carrying out an inverse coordinate system transformation, the results can be transformed into the original computational domain. Benefitted from the coordinate system transformation method, semi-analytical elements can be applied to solve the singularities in potential problem with respect to any kinds of material properties. Accurate physical fields as well as the first three singular coefficients can be arrived at the same time.