Magnetic Field Analyses by Using Free Mesh Method and Their Visualization

netron sputtering system. The numerical analyses by using the finite element method (FEM) are applied in various fields. In FEM, the pre-processing such as a mesh generation is a complicated procedure. Yagawa et al. introduced the free mesh method (FMM), which is a kind of the meshless methods. 1), 2) In the electromagnetic analysis, the FMM was applied in Refs. 3) and 4). In order to obtain more accurate solution efficiently in such problems, the distribution of nodes has to be dense in a region where the change of the potential distribution is large. It is necessary to distribute the nodes adaptively to examine the proper profiles of electromagnetic features. In this study, the magnetic field analysis is carried out in the magnetron sputtering system shown in Fig. 1. In order to solve the magnetic field accurately and efficiently, the distribution of nodes used in the FEM calculations should be changed adaptively due to the vector potential distribution or magnetic field configuration. The estimation of the values of the magnetic flux density is carried out in the FMM to get the distribution of nodes adaptively. The indicator is the difference of the value on the node from the average one inside the element. The adaptive subdivision of nodes is carried out by using this estimation. 5)