Study On The Coupled Finite Element-Element Free Galerkin Method For Electromagnetic Field

Currently, Finite Element Method (FEM) is the most essential method for electromagnetism field calculation. And some FEM's drawbacks can hardly be ameliorated by the improvement of itself. For example: the numerical scatter of FEM is on the base of meshing the whole computational area into many small elements. Thus, in computing some complex areas, A large number of elements and sometimes remeshing is needed in order to avoid big obtuse angles or small acute angles. This increases the difficulty of FEM prestage handling. On the contrary, the Element Free Galerkin Method (EFGM), which also called Meshless Method (MLM) only needs node information, is a new powerful method for electromagnetism field calculation. For the EFGM does, not need element information, it can fetch up some disadvantages of FEM. But EFGM is arranged by Moving Least Square Approximation (MLSA), so it is difficult to solve essential boundary conditions.Hence, we can couple the FEM and EFM to solve electromagnetism problems. Because of the coupled method can take the advantage of both methods, it can not only ensure the accurate but also can guarantee the efficiency of the computation. To be a new numerical algorithm, Coupled FEM and EFM has great latent capacity. This study has very extensive theoretic and realistic meanings for the electromagnetism field computation.The Coupled FE-EF Method is a new numerical computation method that based on the FEM and EFM. It's main difficulty is how to handle intermediate section, which derive some different Coupled FE-EF Methods. In this paper, four different coupled methods will be studied in electromagnetic field, especially which based on Lagrange Multiplier.The main idea of Couple method which base on Lagrange Multiplier: The computational field should divided into two parts, FEM and EFM domain, separately. This can avoid complex handling of intermediate domain. It can be achieved by add Lagrange Multiplier to electromagnetic fonctionelle. By the way, the corresponding theoretical formula has beenderived in the third chapter, and be verified in some electromagnetic numerical computation. It is proved that Coupled FEM and EFM can be used in electromagnetic fields.