Research On Meshless Domain Decompostion Methods For Electromagnetic Problems

Mesh-free method that only requires node information without the need for topology information between nodes, gained more and more attention in the calculation of the electromagnetic problems. But when encounter the non-uniform complex medium as well as the irregular shape model problem, a simple element-free method is unable to meet the needs. In this paper, domain decomposition method with different cell-free method coupling, a more systematic discussion of the static field of the electromagnetic field numerical calculation of these coupling methods, time-harmonic field and transient field, and apply it to electromagnetic generator rotor interturn short circuit-force characteristics of the computational analysis. Full text of the main work consists of the following areas:1. Study on overlapping and non-overlapping domain decomposition method with meshless method of the coupled solver, followed by improved does not require iterative domain decomposition method with meshless method of coupling and its application to the solution of differential equations, derivation process in detail.Because radial basis function (RBF) method is a very important branch in the meshless methods, so we choose the multiquadrics (MQ), inverse multiquadrics (IMQ) and Gaussians RBF as an example. Comparing with common decomposition meshless method, we found that the range of the shape parameter C in RBF is extended by using the improved decomposition method. It makes the choice of shape parameter c is relatively easy. Secondly we are rearranging nodes on the interface surfaces, which makes the original solution of various areas of cumulative error received some offset, and this is the reason for the improved decomposition of element-free method has high precision.2. Coupling element-free method with domain decomposition, and applied it to solve static electromagnetic fields problems, including two sub-regions and multi-sub-regions conditions. The simulation results indicated that, the improved decomposition method with meshless method can model the electromagnetic characteristics on the interface. We also applied it to the analysis of rotor short circuit in a turbo-generator, which involves different regions, such as air gap region, copper region and iron region. 3. A complex coefficient radial basis function (RBF) collocation method to solve the problem of quasi-static eddy field is presented in this paper. According to the different meanings of real part and imaginary part in the complex of the harmonic field calculation, we selected different scales of RBF and discussed the multiquadric (MQ) RBF collocation detailedly. The study formed complex coefficients RBF collocation method for quasi-static eddy problems which included the method's principles, discrete model and implementation procedure. In the metal long square column example, the analytical solution and the numerical solution are compared, the simulation results show that the complex coefficients RBF collocation method is correct and effective.4. Coupling element-free method with domain decomposition, and applied it to solve transient electromagnetic fields problems. We derivate the relevant process and give the specific solution steps, And preliminary discussion on its application to steam turbine-generator turn to turn short circuit condition in the calculation of transient electromagnetic problems.