Singularity Extraction Method Research Articles

An efficient and highly accurate singularity extraction method for the evaluation of transient potentials of stratified media

AbstractAn efficient and highly accurate method for extracting the singularity of scalar potential time‐domain Green's function (TDGF) of layered media is presented. The proposed method is based on the Taylor series expansion and is exploited in the finite‐difference (FD) technique. The presented method is accurate for the singularity behavior of the potential near the source. Also, the effect of singularity extraction box size on the calculation error of Green's functions is explained. Numerical results demonstrating the accuracy of the proposed singularity extraction method for calculating the TDGF of a PEC‐backed dielectric slab are presented. It is shown that the accuracy of the evaluated TDGF is improved by an order of magnitude using the proposed singularity extraction technique. Also, the effect of changing the spatial and temporal steps of the FD scheme on the calculation error is studied.

A Thin-Layer Volume Integral Equation Formulation for Linear and Non-Linear Magnetostatic Problems

A thin-layer approximation of the magnetostatic volume integral equation (VIE) method is presented. This method, referred to as the thin-VIE (TVIE), utilizes a thin approximation of Green’s function. The TVIE approximates both the transverse and the normal magnetization in the material represented by a surface mesh, dramatically improving the accuracy of the method. The TVIE is solved via a locally corrected Nystrom formulation, supporting high-order meshing and solution accuracy. A high-order singularity extraction method is used to compute the hypersingular terms required by near-field local corrections, leading to a very efficient algorithm. The method is applied to linear media, as well as non-linear, anisotropic, and hysteretic medium. The method is also hybridized with the VIE method, allowing for mixed meshes for solving general problems.

Efficient and versatile surface integral approach to light scattering in stratified media.

Recent advances in nano-optics elicit a growing need for more efficient numerical treatments of light-matter interaction in stratified backgrounds. While being known for its many favorable properties, usage of the surface integral approach is hindered by numerical difficulties associated with layered-medium Green's functions. We present an efficient and robust implementation of this approach, addressing the limiting issues. The singularity extraction method is generalized to account for the occurring secondary-term singularities. The resulting scheme thus allows for arbitrary positioning of the scatterers. Further, the laborious matrix-filling process is dramatically accelerated through a simple and robustly-devised, spatial interpolation scheme, completely devoid of integral evaluations. The accuracy and versatility of the method are demonstrated by treating several representative plasmonic problems.

A Numerical Method for Modeling the Effects of Irregular Shape on Interconnect Resistance

When clock frequencies exceed gigahertz, the skin depth in analog and digital circuits greatly decreases. The irregular shape of the cross section of the interconnect plays an increasingly important role in interconnect parasitic extraction. However, existing methods only focus on the rough surface of the interconnect, while ignoring other irregular shapes, such as the trapezoidal cross section. In this work, a new simulation method is proposed for irregular interconnects, which is applicable to arbitrary irregular shapes and to a wide range of frequencies. The method involves generating a mesh information file firstly and then extracting the frequency-dependent resistance based on a numerical solution of scalar wave modeling by using the method of moments. The singularity extraction method is used to calculate the self-inductors. The data from experiments verify the accuracy of our proposed method.

A Practical Implementation and Comparative Assessment of the Radial-Angular-Transform Singularity Cancellation Method

A practical numerical integration approach is proposed for the radial-angular-transform singularity cancellation (SC) method such that all singular and near-singular integrals encountered in the method-of-moments (MOM) solution of integral equations are evaluated to arbitrary pre-specified error levels. In the proposed approach, the transformed MOM integrals are evaluated using the progressive Gauss–Patterson quadrature rules that provide on-the-fly error estimates; these error estimates are used to automate the choice of quadrature rules in the SC method whose performance strongly varies from one impedance matrix entry to another. This progressive numerical integration approach is carefully compared to a naïve implementation of the SC method that uses static quadrature rules as well as to the more common singularity extraction (SE) method. Specifically, the SC and SE methods are applied to the classical solution of the frequency-domain electric field integral equation using RWG basis functions and several scattering problems are solved in the low- and high-frequency regimes of analysis. Numerical results show that although the proposed approach improves the efficiency of the SC method significantly, the SE method, especially if high-order asymptotic forms of Green functions can be extracted, remains the most efficient alternative when applicable.

Efficient and accurate multi-layered elastostatic Green's functions via the bi-material Green's function

The three-dimensional elastostatic Green's functions for multi-layered half-spaces are expressed in terms of a cylindrical system of vector functions using the propagator matrix method. To obtain efficient and accurate results near the singularity at the interface between layers, the singularity extraction method is employed in the transform domain, based on the singular solutions for the bi-material full space expressed here in vector cylindrical function form. Numerical trials demonstrate that this approach improves on previous work, which relied on singularity extraction based on the well-known singular (Kelvin) solution for the homogenous full-space. A boundary element implementation illustrates the practical potential of this work to boundary value problems.

Singularity of the magnetic-field Integral equation and its extraction

In the solution of the magnetic-field integral equation (MFIE) by the method of moments (MOM) on planar triangulations, singularities arise both in the inner integrals on the basis functions and also in the outer integrals on the testing functions. A singularity-extraction method is introduced for the efficient and accurate computation of the outer integrals, similar to the way inner-integral singularities are handled. In addition, various formulations of the MFIE and the electric-field integral equation are compared, along with their associated restrictions.

On the numerical calculation of the magnetic current frill model

The numerical calculation of the singular electric field from a magnetic current frill is reexamined with respect to two types of coaxially fed wire antennas. It is shown that the moment method with the Galerkin matching procedure allows direct and efficient numerical integrations to yield accurate results on the input impedance without any special singularity extraction methods. This demonstrates a simple but efficient and accurate method for the calculation of the input impedance of wire antennas by using the magnetic current frill excitation model. Numerical results on the fast convergence of the input impedance are presented.