Implementation Of Calderón Preconditioned Integral Equation For Open Targets

The electric field integral equation(EFIE)can be chosen for the electromagnetic scattering problem of the open perfectly conducting(PEC)surface.However,the condition number of the corresponding matrix equation of the method of moments is relatively high,being not suitable for iterative solution,even if the surface is closed.How to overcome this problem has been a hot topic in computational electromagnetics.In recent years,Calderón preconditioned integral equation method,a analytically preconditioned integral equation method,has been received wide attention,and many results about it have been achieved.In this paper,we investigate the implementation of Caledon preconditioner for the EFIE on open PEC surface.The EFIE is a first kind Fredholm integral equation,and the convergence of an iterative solver used for its numerical discretization form is poor.Calderón precondition is a possible so-lution for this problem.Using the property of the projection operator,we can derive Calderón's identity.By means of its physical interpretation,we can know that this preconditioning method can be applied to open PEC surface theoretically.However,such an integral equation is not suitable for using RWG functions as testing functions.BC functions should be used as testing functions.The matrix equation thus obtained is likely to be well conditioned.This paper in-troduces the implementation of Calderón preconditioned integral equation method for the EFIE on open PEC surface.Numerical examples show that Calderón preconditioner can greatly re-duce the number of iterations.In addition,the FG-FFT algorithm is introduced into Calderón preconditioned integral equation method,which significantly reduces the memory requirements and the solution time.Thus to an extent,we overcome the increasing memory requirements caused by Calderón preconditioner.In this paper,the numerical performance of Calderón pre-conditioner with complex wave number for electromagnetic scattering problems from an open PEC surface is also investigated.The main works are as follows:1.The EFIE on an open PEC surface is preconditioned by Calderón preconditioner.Calderón identity is derived from the properties of the projection operator,and the physical inter-pretation of Calderón precondition method is provided.The physical explanation shows that Calderón preconditioner can be applied to open PEC surface problems.2.Calderón preconditioned integral equation is numerically discretized by using the auxil-iary variables.By introducing BC functions as test functions,the corresponding matrix equation is obtained.Numerical examples show that Calderón preconditioner can greatly reduce the number of iterations when solving an open PEC surface problem,confirming the good effect of Calderón preconditioned integral equation method.3.Calderón preconditioner results in increasing the size of matrix,thus leads to increasing the computation time and the memory requirement.In order to overcome this short-coming,the FG-FFT algorithm is introduced into Calderón preconditioned electric field integral equation method,significantly reducing the computation time and the memory requirement.4.The numerical performance of Calderón preconditioned EFIE on an open surface is inves-tigated.The imaginary part of the complex wave number is taken as the main parameter,and the connection between the convergence rate and the imaginary part of the complex wave number is analyzed through numerical examples.It is concluded that the proper complex number can further improve the convergence of the mentioned algorithm.