A Research On The Combined Source Algorithm For Electromagnetic Scattering Problems

The combined source integral equation(CSIE) is an electromagnetic simulation algorithm.The method of moments(MoM) is a method of converting linear integral equations into matrix equations and then solving matrix equations.MoM is commonly used in electromagnetic scattering and radiation problems in the low frequency region.Rao-WiltonGlisson(RWG) basis function can discretize the electric current and magnetic current on the surface of a perfect electrical conductor(PEC).Combining the CSIE and Mo M can solve the electromagnetic scattering problem of PEC in the low frequency region.Among the commonly used electromagnetic simulation methods,the electric field integral equation(EFIE) is considered to have the highest calculation accuracy.But the algorithm convergence is not good.On the contrary,the magnetic field integral equation(MFIE) has the best convergence performance,but there are large errors.The most commonly used algorithm for PEC scattering is the combined filed integral equation(CFIE).Because CFIE has the best overall performance.As a companion method of CFIE algorithm,CSIE algorithm has higher accuracy than CFIE algorithm and no internal resonance.The main content of this thesis is CSIE.First of all,this thesis refers to two latest papers as the basis for implementing the algorithm.Secondly,this thesis proposes two improvements for some problems in the numerical processing.It is proposed to widen the value range of the weighting factor to the complex domain to speed up the solution convergence.Thirdly,Razor-Blade test function is used to simplify the matrix filling process in order to simplify the calculation.Finally,several multi-scale calculation examples are used to verify the improvement method proposed in this thesis.The full text structure of this thesis is as follows:First,we give a brief introduction to the current research background and research status of computational electromagnetics.Second,Mo M,Galerkin method and other numerical methods used in the implementation of CSIE algorithm are explained in detail.Third,the related theories and formulas relate to CSIE algorithm are described and deduced here.And Mo M is combined to calculate the electromagnetic simulation results of some examples.Fourth,the order of solving electric current and magnetic current is changed to reduce one-time consumption of computer resources.It is proposed to use Razor-Blade test function to simplify the CSIE derivation process.Fifth,it is proposed to use complex domain weighting factors to improve the CSIE equations.And put forward the angle that can use the multi-scale problem to analyze the stability of the improved algorithm.Sixth,this chapter summarizes the full thesis.And the future work of CSIE is prospected.