# Fast Green Function Evaluation for Method of Moment

## TL;DR

This paper introduces an adaptive interpolation method to accelerate Green function evaluations in the Method of Moments, significantly improving computational efficiency while maintaining accuracy.

## Contribution

The paper presents a novel adaptive interpolation approach for fast Green function evaluation in MOM, reducing computation time by over 20% with minimal accuracy loss.

## Key findings

- Achieves over 20% efficiency improvement in MOM calculations.
- Maintains high accuracy with rigorous error bounds.
- Easily integrable into existing MOM codes.

## Abstract

In this letter, an approach to accelerate the matrix filling in method of moment (MOM) is presented. Based on the fact that the Green function is dependent on the Euclidean distance between the source and the observation points, we constructed an efficient adaptive one-dimensional interpolation approach to fast calculate the $Exp$ type function values. In the proposed method, several adaptive interpolation tables are constructed based on the maximum and minimum distance between any two integration points with local refinement near zero function values to minimize the relative error. An efficient approach to obtain the sampling points used in the interpolation phase is carefully designed. Then, any function values can be efficiently calculated through a linear interpolation method for Exp and a Lagrange polynomial interpolation method for the Green function. In addition, the error bound of the proposed method is rigorously investigated. The proposed method can be quite easily integrated into the available MOM codes for different integration equation (IE) formulations with few efforts. Comprehensive numerical experiments validate its accuracy and efficiency through several IE formulations. Results show that over 20% efficiency improvement can be achieved without sacrificing the accuracy.