# ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations

## TL;DR

This paper explores the use of ParaExp, a parallel-in-time method, combined with Leapfrog integration to efficiently simulate high-frequency electromagnetic wave problems, demonstrating its effectiveness on toy and realistic models.

## Contribution

It introduces a novel combination of ParaExp with Leapfrog for electromagnetic simulations, enhancing parallel efficiency for high-frequency wave problems.

## Key findings

- Effective parallelization of electromagnetic simulations
- Successful application to realistic spiral inductor model
- Improved computational efficiency demonstrated

## Abstract

Recently, ParaExp was proposed for the time integration of linear hyperbolic problems. It splits the time interval of interest into sub-intervals and computes the solution on each sub-interval in parallel. The overall solution is decomposed into a particular solution defined on each sub-interval with zero initial conditions and a homogeneous solution propagated by the matrix exponential applied to the initial conditions. The efficiency of the method depends on fast approximations of this matrix exponential based on recent results from numerical linear algebra. This paper deals with the application of ParaExp in combination with Leapfrog to electromagnetic wave problems in time-domain. Numerical tests are carried out for a simple toy problem and a realistic spiral inductor model discretized by the Finite Integration Technique.