The Fast Algorithm For Solving The Electromagnetic Properties Of Multiple Bodies Of Revolution

Body of revolution(BoR)is a rotationally symmetric 3-D object formed by rotating a planar curve around the axis of symmetry.The BoR objects widely appear in many practical engineering applications.The analysis of radiation and scattering from those structures like radome or missile are urgently demanded by the engineers.Fortunately,a special method: Method of moment for body of revolution(BoR-MoM)has been proposed for solving the electromagnetic properties from this kind of objects.Taking the advantage of the characteristic of rotational symmetry,the 3-D BoR problem can be reduced into a series of 2-D problems.By this scheme the computation complexity to solve the problem is greatly reduced.The contents of this thesis are based on the BoR-MoM and contains five parts as follows:The first part of this thesis is a brief review of the BoR-MoM.This chapter starts from the surface equivalent principle,and the following is to introduce the derivation of the surface integral equation(SIE),the principle,and the formulas of BoR basis function.The method to eliminate the singularity of BoR basis functions and the formula to decide the number of mode are also given in this part.At last the results of scattering from perfect electric conductor(PEC),dielectric and composite BoR is demonstrated to show the accuracy and efficiency of the method.The next part of the thesis introduces the spectral integral method for the scattering from multilayer smooth BoR objects,which is named BoR-SIM.In the BoR-SIM,the current along the generatrix of BoR is expanded by the Fourier series.According to the Nyquist theorem,two sampling points per wavelength are adequate to achieve a reasonable accuracy,compared with eight to ten points per wavelength when applying the conventional BoR-MoM.Consequently,this method can greatly reduce the CPU time.The BoR-SIM can be seen as an alternative method of conventional BoR-MoM,and be utilized in many applications that conventional BoR-MoM used to be utilized.The next two parts of this thesis are to introduce two methods to solve the multiple BoRs problems: the characteristic basis function method for multiple BoRs(BoRCBFM)and the multi-region iterative method for multiple BoRs(BoR-MRIM).The BoRCBFM is developed from the conventional characteristic basis function method(CBFM).When CBFM is engaged in solving multiple BoRs problems,the mode characteristic basis function is adopted in order to reduce the time for generating the characteristic basis functions.In addition,the basis function mapping technique(BFMT)is applied to solve the RWG basis function coefficients by the BoR basis function coefficients.By applying this technique,MLFMA can be used to expedite the matrix-vector multiplication.In addition,a sparsification technique is used to further improving the efficiency of the BoR-CBFM.The BoR-CBFM is a efficient method for calculating the scattering from multiple BoRs especially in calculating the multiple right-hand-term problems because of the greatly reduction of the number of unknowns.The other method for multiple BoRs problems,the so called BoR-MRIM is based on the ”divide and conquer” philosophy.The method divided the scattering problem from multiple BoRs into separately independent BoR problems.These single BoR problems can be solved by the conventional BoR method or BoR-SIM.Then calculate the interaction between different BoRs via the iteritive solver.The BoR-MRIM is a very efficient method to solve the scattering and radiation from multiple BoRs.Compared with the BoR-CBFM,it has more advantages in solving single right-hand-term problems.The fifth part of the thesis introduces the application of the BoR-SIM and the BoRMRIM in solving the local surface plasmon resonance(LSPR)effect of nanoparticles.LSPR is a particular resonance effect that only observed in nanoparticles and is widely used in many engineering regions.In this chapter some special optimizing schemes on BoR-SIM and BoR-MRIM for solving LSPR problems is introduced.After optimization,these two BoR methods can achieve great efficiency,accuracy and adaptation.The numerical results demonstrate the ability of these optimized methods to make qualitative and quantitative analysis for LSPR of nanoparticles.The content of this thesis focuses on the BoR methods.The spectral method and several kind of domain decomposition methods are involved to solve single and multiple BoR problems combined with the BoR basis functions.The deepgoing and systematic study on efficient methods for multiple BoR basis functions are given in this thesis.The study in this thesis provides effective solution for engineering requirements in many aspects.