Measured Equation Of Invariance Coefficients Research Articles

Measured equation of invariance with non-uniformly distributed line sources as metrons

In the paper, δ functions are employed as simple yet effective metrons to generate measured equation of invariance (MEI) coefficients in the MEI method. Compared with the widely used sinusoidal functions, δ functions greatly reduce the time for the computing of measuring functions and alleviate the ill-conditioning phenomenon of the matrix equations for the determination of MEI coefficients, hence enabling one to interrelate more nodes in the MEI. In this way, the accuracy of the solutions for electrically large scatterers can be improved progressively. It is also found that non-uniformly distributed δ metrons produce more accurate and stable results compared to uniformly distributed metrons. Numerical results for two-dimensional scattering problems are presented to show the accuracy and efficiency of the proposed method.

Applicability of Insensitive Properties of Measured Equation of Invariance Coefficients for Modified Scattering Objects

The applicability of insensitive properties of measured equation of invariance (MEI) coefficients for the computation of scattering from modified structured bodies is presented in this letter. During scattering computation by using MEI technique (in IE-MEI or SIE-MEI method), the MEI coefficients of the whole scatterer is calculated in the conventional method. In contrast, using the insensitive properties of the MEI coefficients, the new method calculates the MEI coefficients only around the modified area if some portion of the scatterer is modified and reuse those for the other portion of the scatterer. Thus CPU time for solving the modified problem can be saved by using the new method. The numerical results verified the validity of the new technique which is compared with the available numerical solutions.

An iterative algorithm based on the measured equation of invariance for the scattering analysis of arbitrary multicylinders

It is known that the measured equation of invariance (MEI) is generally valid for outgoing waves just as other absorbing boundary conditions (ABCs). However, for the scattering problem of multicylinders, the scattered field from one cylinder is just the in-going incident wave to other cylinders. So the MEI cannot be directly applied to the scattering problem of multicylinders. In this paper, an iterative algorithm based on the MEI is first proposed for the scattering problems of multicylinders with arbitrary geometry and physical parameters. Each cylinder is coated with several layers of meshes and the MEIs are applied to the truncated mesh boundaries. It has been demonstrated that the MEI can truncate the meshes very close to the surfaces of the cylinders and then results in dramatically savings in memory requirements and computational time. The MEI coefficients of each cylinder can be stored and reused to form the sparse matrices during each iteration procedure as they are independent of excitations. So more central processing unit (CPU) time is saved as the MEI coefficients are calculated only once in the algorithm. The method can be applied to problems of various kinds of multiple cylinders with arbitrary configurations and cross sections. Numerical results for the scattered fields are in good agreement with the data available. Finally, examples are given to show the iterative algorithm applicable to electrically large multicylinders coated with lossy media.

Validity of the measured equation of invariance

The measured equation of invariance (MEI) is derived without any postulates. It is shown that the coefficients of the MEI are invariant to the field of excitation. However, the accuracy of the MEI solution is closely related to the number of nodes in the MEI. Coupling more nodes improves progressively the accuracy of the MEI solution. With increasing nodes, the matrix problem for the determination of the MEI coefficients becomes seriously ill conditioned and generally must be solved using multiple precision arithmetic. The consequences of the ill-conditioning phenomenon are discussed.

Application of discrete periodic wavelets to measured equation of invariance

Recently, the wavelet expansions have been applied in field computations. In the frequency domain, the application is focused on the thinning of matrices arising from the method of moment (MoM). The thinning of matrices can best be done by the measured equation of invariance (MEI), which provides sparsity almost without sacrificing accuracy in that the boundary equation it entails is convertible to that of the MoM. The real power of the wavelet expansions is to give high resolution in convolution integrals. High resolution is also needed in the process of finding the MEI coefficients, which are obtained via an integration process almost identical to that of the MoM. In this paper, it is shown that when the fast discrete periodic wavelets (FDPW) are used as metron currents in the MEI method, the resolutions of the MEI coefficients are improved at high-frequency computations or at geometric extremities. The level of sparsity of the MEI is much more favorable than that achievable by the thinning of MoM matrix using the wavelet expansions. The role of FDPW in the MEI happens to be more fitting than its place in the MoM.

On the measured equation of invariance for an electrically large cylinder

By considering the electromagnetic scattering of a circular conducting cylinder, the accuracy of the measured equation of invariance (MEI) is examined analytically. Using the asymptotic expansions of the Hankel's functions of second kind, H/sub n//sup (2)/(k/spl rho/) as measuring functions, the case of an electrically large cylinder is studied. It is shown that the MEI coefficients are invariant to the field of excitation.