Research On The Multi-Grid Method Applied To Numerical Calculation Of Engineering Magnetic Field Problems

This thesis mainly researches on the application of multi-grid method for the numerical calculation of engineering magnetic field problems.Many complicated numerical analyses of the engineering magnetic field problems, e.g. the coupled problem of magnetic and flow fields and the magnetic field problem of 3D model, can be expressed as the partial differential equation problems for determining solution. However, these partial equations are usually non-time-invariant and nonlinear. Their numerical solutions not only need huge computational cost, but also involve many numerical techniques. Furthermore, it usually takes most of the whole computation time to solve the resultant algebraic equations deduced in the problems. As a rapid algorithm, the multi-grid method has been used to solve the resultant equations from the discretization of the partial differential equations with much less computation time. The principle of the method is that using certain of the grids with different interval can eliminate the error components of different frequencies, the fine grid for the error components of higher frequency, while the rough grid for the one of lower frequency.The theory of multi-grid method has been rather mature through the development of the recent 30 years. For the engineering application of the method, most of contributions published are focus on fluid mechanics. In the last few years, multi-grid method applied to the static electric field and flow field has made some achievement. But there are few contributions shown about the application of multi-grid method in the magnetic and the coupled problem of magnetic and other physical field. In this thesis, the multi-grid method and finite volume method are combined and applied to the calculation of the magnetic field and the coupled problem of magnetic field and flow field. The computer program is programmed by Visual Fortran. The calculation of the Poisson equation which has analytic solution has testified that the program programmed is correct. Lastly, the contrast of multi-grid method with improved triangle decomposition method and SOR (successive over-relaxation iteration) algorithm are carried out and the results show that the multi-grid method can converge fast and hence large saving in CPU time.