Natural Element Method In Electromagnetic Field Numerical Calculation

The Finite Element Method (FEM) has been widely used in the numerical calculation of electromagnetic field, but on the hand of adaptive calculation or inverse problem of electromagnetic field design, the FEM pre-processing or mesh generation cost long time and more works. The Natural Element Method (NEM) can solve these issues effectively, it needs only the points information but not the cell or grid information, totally avoiding the troubles of pre-processing grid in FEM, it is convenient to realize the adaptive analysis of electromagnetic field. This paper mainly research on the feasibility of NEM in processing electromagnetic field.Firstly, this paper deeply researches on the electromagnetic field numerical calculation methods based on FEM, it also describes the establishment of the FEM system equilibrium equations based on the Galerkin and Petrov-Galerkin.Secondly, starting from the electromagnetic field numerical calculation based on FEM, combined with the relative theories of electromagnetic field and NEM, this paper deduces the functions in electromagnetic field numerical calculation based on NEM. The natural neighbor interpolation function is constructed with theδcharacteristic, and it is strictly linear on the border of the points in the adjacent, so the NEM can easily impose the essential boundary conditions, also can easily deal with its boundary surface. The system equilibrium equation based on the Galerkin needs three or more integral pitch winding points in background triangle integral grid to accomplish numerical integration, so this makes the calculation process complicated and long time consumed, so this paper uses the system equilibrium equation based on Petrov-Galerkin. The integral of this method can be finished directly in sub-domain, no additional background integral grid, and the central of triangle integral grid only needs one point to accomplish numerical integral, simplifying the calculation process and saving the time.Finally, this paper takes the example of the electromagnetic field issues with linear analytical solution, compiles corresponding Fortran programs, uses NEM to accomplish electromagnetic field numerical calculation. According to the example result, the conclusion is available: compared with the FEM, the NEM has high precision and more close to analytical solution, the NEM can reach high precision with fewer units. Therefore, this paper successfully brings the NEM to electromagnetic field numerical calculation.