Research On Higher Order MoM And Fast Algorithms For Electromagnetic Scattering And Radiation From Metallic And Dielectric Targets

In recent years,with the rapid development of science and technology,electromagnetic modeling from the complex structure targets is often required in many fields,such as target detection and recognition,stealth and anti-stealth technology,design and evaluation of radar system,high-performance antenna system design,microwave integrated circuit simulation and electromagnetic compatibility analysis,etc.To solve this problem,this dissertation thoroughly studies the key techniques and high efficient numerical solutions of integral equation based on higher order the method of moments(MoM)and fast algorithms for electromagnetic scattering and radiation from metallic and dielectric targets.According to the equivalence principle,the surface integral equation(SIE),volume integral equation(VIE)and volume surface integral equation(VSIE)are established firstly.Then,the numerical simulation and key technologies of MoM are elaborated systematically.This part presents the higher order geometrical modeling which is based on curved triangular elements and curved tetrahedral elements,and gives the commonly utilized lower order basis functions for expanding the currents on metallic surface and the equivalent electric and magnetic currents inside dielectric volume.Finally,the commonly used excitation methods and the associated electromagnetic parameters(e.g.,radar cross section and input impedance)are introduced.To effectively reduce the number of unknowns,the integral equation higher order MoM(IE-HO-MoM)based on higher order hierarchal vector(HOHV)basis functions is studied.Firstly,a set of HOHV basis functions with good orthogonal which is defined on curved tetrahedrons is ulitized to discretize VIE,and that given the name of the volume integral equation higher order MoM(VIE-HO-MoM).In the research process,the deduction of these HOHV bases,the continuity and orthogonal analysis,the hybrid modeling technique based on the HOHV bases and Duffy transform method for removing the singularity in curved volume integrals are respectively studied in detaill.Based on VSIE-HO-MoM,the volume surface integral equation higher order MoM(VSIE-HO-MoM)which is based on HOHV is proposed,and it is used to analyze electromagnetic scattering and radiation by electrical-large size composite metallic and dielectric targets.In different IE-HO-MoM,for different orders of HOHV bases,the cal-culation parameters including the average mesh size and the number of gauss integral points,which have great effect on the efficiency and accuracy of solution results,are discussed deeply.And finally the optimization selection principle for IE-HO-MoM is given.Numerical examples illustrate that through reasonably choosing the basis' s order,the mesh size of discretization elements and the number of Gaussian integral points,IE-HO-MoM can result in the decrease of unknowns,and obtain high precision and calculation efficiency simultaneously.Moreover,the hybrid modeling technique can further improve the utilization of the computer resources in higher order methods.In order to accelerate the iterative solution procedure of higher order MoM,the MLFMA algorithm is presented.The algorithm is respectively combined with SIE,VIE and VSIE for the analysis of typical scattering and radiation problems,which demonstrates the accuracy and efficiency of the higher order MLFMA algorithm.This part mianly focuses on the calculation parameters selection principle of higher order MLFMA and the sparse approximate inverse(SAI)preconditioning technique.Numerical examples shown that through reasonably choosing the basis' s order and the mesh size of discretization elements,higher order MLFMA can effectively enhance the computational efficiency.In practical electromagnetic engineering problems,applying the conformal grids to discretize complex structures not only results in difficulty for the geometric modeling,but also generates additional unknowns.In order to alleviate this problem,this thesis proposes the nonconformal integral equation higher order MoM(NC-IE-HO-MoM),whichi is based on HOHV bases.This nonconformal scheme includes the nonconformal surface integral equation higher order MoM(NC-SIE-HO-MoM),nonconformal volume integral equation higher order MoM(NC-VIE-HO-MoM)and nonconformal volume surface integral equation higher order MoM(NC-VSIE-HO-Mo M).This part mainly focuses on the HOHV basis functions,the basic theory and the implementation process for NC-IE-HO-MoM.Numerical examples show that these nonconformal methods with nonconformal discretizations have main advantages in reducing the difficulty of geometric modeling of 3-D complex targets,and enhancing the flexibility and the applications.Besides,a basis function expansion and recommendation(BER)technique is proposed to accelerate the speed of fill-in the impedance matrix elements in IE-HO-MoM,and the efficiency of the BER technique has been demonstrated by numerical examples.In many practical applications,how to quickly and effectively analyze the wideband radiation characteristic and wideband scattering characteristic of a target is a very interesting problem.This thesis presents the fast methods for wideband frequency scanning and wideband medium parameter scanning.Based on the Taylor series expansion(TSE)technique,the technique is combined with SIE,VIE and VSIE,respectively,and the integral equation methods based on TSE technique is derived.These wideband algorithms are empolyed to solve wideband electromagnetic response from conducting,dielectric and mixed conducting-dielectric targest.Numerical results demonstrates the efficiency and accuracy of the method.In order to avoid the problem that using TSE technique producing high memory requirements results in its application scope,the higher order wideband algorithm with HOHV basis functions is proposed.Numerical examples show that the accuracy,the efficiency and the universality of the algorithm.As a basic research on the electromagnetic scattering and radiation problems of arbitrarily shaped 3-D complicated objects,our research presented in the thesis has provided a powerful approach in rigorous electromagnetic modeling and fast solution.A set of numerical codes has been independently developed,which is integrated with a variety of efficient solution methods and has good platform portability and reusability.Their accuracy and efficiency are demonstrated by numerical results,which provides an a solid method foundation to further solve electromagnetic problems in practical engineering.