# Symmetric Numerical Integration Techniques for Singular Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation

@article{Freno2019SymmetricNI, title={Symmetric Numerical Integration Techniques for Singular Integrals in the Method-of-Moments Implementation of the Electric-Field Integral Equation}, author={Brian A. Freno and William A. Johnson and Brian Zinser and Donald R. Wilton and Francesca Vipiana and Salvatore Campione}, journal={arXiv: Computational Physics}, year={2019} }

In this paper, we present two approaches for designing geometrically symmetric quadrature rules to address the logarithmic singularities arising in the method of moments from the Green's function in integrals over the test domain. These rules exhibit better convergence properties than quadrature rules for polynomials and, in general, lead to better accuracy with a lower number of quadrature points. We demonstrate their effectiveness for several examples encountered in both the scalar and vector…

## One Citation

### Symmetric Triangle Quadrature Rules for Arbitrary Functions

- Computer ScienceComput. Math. Appl.
- 2020

## References

SHOWING 1-10 OF 26 REFERENCES

### All-Analytical Evaluation of the Singular Integrals Involved in the Method of Moments

- MathematicsIEEE Transactions on Antennas and Propagation
- 2018

Surface integral equation methods routinely require the integration of the singular Green’s function or its gradient over basis functions (BF) and testing functions (TF). Many techniques have been…

### Hybrid Integration Scheme for the Evaluation of Strongly Singular and Near-Singular Integrals in Surface Integral Equations

- MathematicsIEEE Transactions on Antennas and Propagation
- 2019

The accurate and efficient evaluation of surface source integrals is a key step in obtaining reliable solutions to electromagnetic problems using integral equation formulations. In this paper, we…

### Numerical Evaluation via Singularity Cancellation Schemes of Near-Singular Integrals Involving the Gradient of Helmholtz-Type Potentials

- MathematicsIEEE Transactions on Antennas and Propagation
- 2013

In this paper, we present a purely numerical procedure to evaluate strongly near-singular integrals involving the gradient of Helmholtz-type potentials for observation points at finite, arbitrarily…

### Optimized Numerical Evaluation of Singular and Near-Singular Potential Integrals Involving Junction Basis Functions

- Physics, MathematicsIEEE Transactions on Antennas and Propagation
- 2011

In analyzing conducting bodies composed of surfaces connected to wires via a method of moments discretization of the electric field integral equation, junction basis functions are defined at…

### DIRECTFN: Fully Numerical Algorithms for High Precision Computation of Singular Integrals in Galerkin SIE Methods

- MathematicsIEEE Transactions on Antennas and Propagation
- 2013

Fully numerical schemes are presented for high precision computations of the four-dimensional integrals arising in Galerkin surface integral equation formulations. More specifically, the focal point…

### Evaluation of 4-D Reaction Integrals Via Double Application of the Divergence Theorem

- Mathematics, Computer ScienceIEEE Transactions on Antennas and Propagation
- 2019

A scheme for evaluating 4-D interaction integrals between pairs of arbitrarily positioned and oriented elements using the surface divergence theorem and is numerically validated for static and dynamic kernels arising in the electric field integral equation.

### Singularity of the magnetic-field Integral equation and its extraction

- MathematicsIEEE Antennas and Wireless Propagation Letters
- 2005

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…

### Generalized Gaussian quadrature rules for systems of arbitrary functions

- Mathematics
- 1996

A numerical algorithm is presented for the construction of generalized Gaussian quadrature rules, originally introduced by S. Karlin and W. Studden over three decades ago. The quadrature rules to be…

### Numerical evaluation of singular and near-singular potential Integrals

- MathematicsIEEE Transactions on Antennas and Propagation
- 2005

A simple and efficient numerical procedure using a singularity cancellation scheme is presented for evaluating singular and near-singular potential integrals with 1/R singularities. The procedure not…

### A Family of Augmented Duffy Transformations for Near-Singularity Cancellation Quadrature

- MathematicsIEEE Transactions on Antennas and Propagation
- 2013

A new family of systematically constructed near-singularity cancellation transformations is presented, yielding quadrature rules for integrating near-singular kernels over triangular surfaces. This…