# An efficient steady-state analysis of the eddy current problem using a parallel-in-time algorithm

## TL;DR

This paper presents a parallel-in-time algorithm leveraging harmonic balance for efficient steady-state eddy current analysis, enabling parallel computation of harmonic components to accelerate solutions.

## Contribution

It introduces a novel parallel-in-time method using harmonic balance as a coarse solver for steady-state eddy current problems.

## Key findings

- Successfully applied to a nonlinear coaxial cable model
- Achieved accelerated convergence through parallel harmonic computation
- Validated the method's efficiency for periodic electromagnetic problems

## Abstract

This paper introduces a parallel-in-time algorithm for efficient steady-state solution of the eddy current problem. Its main idea is based on the application of the well-known multi-harmonic (or harmonic balance) approach as the coarse solver within the periodic parallel-in-time framework. A frequency domain representation allows for the separate calculation of each harmonic component in parallel and therefore accelerates the solution of the time-periodic system. The presented approach is verified for a nonlinear coaxial cable model.

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Source: https://tomesphere.com/paper/1905.13076