# Analytically grounded full-wave methods for advances in computational electromagnetics

## TL;DR

This paper presents full-wave methods in computational electromagnetics that guarantee accurate and efficient solutions without needing extra validation.

## Contribution

The paper introduces analytically grounded methods with guaranteed convergence for reliable and efficient electromagnetic simulations.

## Key findings

- The methods provide guaranteed convergence to exact solutions with increasing truncation order.
- They enable highly accurate solutions at low computational cost.
- These solutions can serve as a reference for validating commercial software.

## Abstract

This Theme Issue is a collection of original research and review papers focused on developing a class of well-established and innovative analytically grounded full-wave methods and their applications in computational electromagnetics. These methods are notable for their guaranteed convergence, meaning that the approximate solution obtained by discretizing and truncating the equation governing the problem at hand tends to the exact solution if the truncation order gets larger. Hence, unlike the numerical approximations with no mathematically guaranteed convergence, they do not require post-validation. Moreover, highly accurate solutions are reconstructed with a low computational cost, thus allowing a real-time, precise and exhaustive parametric analysis of various critical structures and complicated physical phenomena. To conclude, the obtained solutions deliver trusted physical results within a reasonable time and without false effects and, therefore, can serve as a reference for validating general-purpose commercial software.

This article is part of the theme issue ‘Analytically grounded full-wave methods for advances in computational electromagnetics’.