The Domain Decomposition Algorithm Based On The Equivalence Principle

Higher requirements are needed for accurate and efficient detection of radar cross section (RCS) with the development of electronic communication.The method of moment(MoM) is a kind of traditional integral equations method, which has been widely used for analysing the electromagnetic scattering problems. The MoM can be used for arbitrary objects with high precision. However, the MoM costs a lot of computer memory. It is too hard to calculate the scaterring of large-scale electromagnetic objects because of the computation limit. Although multilevel fast multipole method (MLFMM) can greatly save the computational resource, it still costs a lot of memories for large-scale objects.Firstly, the domain decomposition method based on the equivalence principle algorithm (EPA) is introduced in the thesis. EPA is used to solve multiscale problems and repeated objects in three dimensions. It is based on the equivalence principle to decompose the solution domain into several parts so that the wave and circuit physics can be separated. Each subdomain is surrounded by an equivalence surface and each equivalence surface is arbitrary. The unknowns in the inside domain are transformed to unknowns on the equivalence surfaces when interfacing with the outer world. The iterative numbers is significantly reduced and the iteration time is greatly saved because of the good impedance matrix’s conditional number.Moreover, the EPA can also be accelerated using attached multilevel fast multipole method (MLFMM) so that large multiscale problems can be solved efficiently.