# Evaluation of Integrals Related to the Magnetic Field Integral Equation Over Bilinear Quadrilaterals

## TL;DR

This paper introduces a new hybrid analytical-numerical method for accurately computing impedance matrix elements in the magnetic field integral equation for bilinear quadrilaterals, achieving high precision even for singular integrals.

## Contribution

The paper presents a novel approach combining analytical and numerical integration to improve accuracy in impedance matrix calculations for BQ geometries in MFIE.

## Key findings

- Achieves up to fifteen significant digits in integral evaluation.
- Effective for self-elements and near-field observation points.
- Applicable to higher-order basis functions.

## Abstract

We present a new method for computing the impedance matrix elements in the method of moments for geometries described by bilinear quadrilaterals (BQ) and for higher-order basis functions (HOBF). Our method is restricted to the Magnetic Field Integral Equation (MFIE) and focuses on the self-elements of the impedance matrix and elements for which the observation point (OP) is near the integration BQ. The method is based on the simple idea of analytical integration along one of the BQ's parameters and numerical integration along the remaining one. For the singular (or nearly so) part of the integral, we show through analysis and examples that our method can provide precision up to fifteen significant digits (SD).

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Source: https://tomesphere.com/paper/1703.02333