NPBS-based adaptive finite element method for static electromagnetic problems

To solve electromagnetic field problems by the finite element method (FEM), it is necessary for users to generate mesh in preprocessing. The quality of mesh, which depends on the quality of set of nodes, strongly affects the accuracy of the analysis result. In this paper, a novel NPBS (node placement method by bubble simulation)-based adaptive finite element method (NPBS-AFEM) was proposed to solve the static electromagnetic problems. The advantages of the NPBS-based AFEM, compared with other known methods, are given as follows: the NPBS-based AFEM not only generates a high-quality nodes set which can be connected to be high-quality meshes, but also uses less DOFs to achieve the required accuracy; this adaptive mesh refinement method can be combined with other a posteriori error estimators to conduct finite element computing; this AFEM can coarsen and refine the mesh in the same framework without manual intervention; it is very suitable to develop the NPBS method in parallel environments due to the short-range force between bubbles; it can be also used to deal with anisotropic problems where the bubbles are replaced by elliptical bubbles. It is shown that the mesh of high quality and higher accuracy than a highly optimized BM (bisection method)-based h-AFEM or uniform refinement method is obtained in three static electromagnetic field problems using the NPBS-AFEM.