Investigation And Application On Overlapping Decomposition Projective Method

With the development of computer technology, computational electromagnetics has been widely applied in communication, rader, electromagnetic protection, electromagnetic compatibility and medical diagnosis, and more and more large scale complex structure electromagnetic problems ocure, when it is used in practical project applications. When the problem is discreted as values, a large amount of unkowns contradict with limited computing resources. Therefore, how to efficiently resolve the large scale complex electromagnetic problems becomes the hot topic of computational electromagnetics. Luckly, the presentation of partitioning algorithm, such as domain decomposition method (DDM) and decomposition projective method (DPM), can transform large scale electromagnetic problem into serveral small scale problems, which provides effective methods for resolving these large scale problems. Besides, as a partitioning algorithm, DPM cannot limited by boundry contions, and is more flexible during parting. The validity and reliability of DPM has been proved in theory and numberical experiments. DPM first resolve problems in sub region, then abtain the numberiacl results of whole region by iterating. However, current DPM needs to iterate more times and takes more time to solve these problems. Based on current DPM, this paper present two-branch overlapping DPM, multi-branch overlapping DPM and fast overlapping DPM. By adding a few of overlapping nodes, these metheds can reduce iteration times and problem resovling time. This paper explains the theories and the implementation procedures of overlapping DPM, and demonstrates these theories. Meanwhile, examples in this paper show the overlapping DPM has improved the computing efficiency. What’s more, the iteration times and computing time have been reduced by 90%.Meanwhile, in order to apply the overlapping DPM to complex electromagnetic problems, this paper firstly combine the overlapping DPM with the subgridding method to analyze and simulate the integrated waveguide (SIW). Some numerical experiments show the flexibility of the combination. This method is not only improve the precision of results but also enhance the efficiency of resolving the large scale complex electromagnetic problems.What’s more, a comparision of the new discretized scheme of 1st Mur’s absorbing boundary condition and measured eguation of invariance (MEI) has been made in this paper. When solving electromagnetic scattering problems, the computational region needs to be truncated. At the truncated boundary, absorbing boundary condition will be set. The absorbing boundary condition determines the scale of unkowns. The numerical results indicate the following conclusions:(1) For small scattering problem, the MEI method is more efficient. (2) For large scattering problem, the new scheme of 1st Mur’s ABC has a great advantage in CPU time consumption. (3) For solving multi-cylinders, the new scheme of 1st Mur’s ABC costs little CPU time, has an acceptable numerical accuracy.