# A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling

## TL;DR

This paper introduces a nested Schur complement solver for Maxwell equations that achieves mesh-independent convergence, improving the efficiency of time domain photonics simulations involving complex boundary conditions.

## Contribution

It presents a novel nested Schur complement approach that effectively solves double saddle point systems with mesh-independent convergence in photonics modeling.

## Key findings

- Achieves mesh-independent convergence in the outer solver
- Efficiently handles elliptic inner systems with various solvers
- Applicable to exponential and implicit time integration methods

## Abstract

A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These linear systems are the so-called double saddle point systems whose structure is handled by the Schur complement solver in a nested, two-level fashion. The solver is demonstrated to have a mesh-independent convergence at the outer level, whereas the inner level system is of elliptic type and thus can be treated efficiently by a variety of solvers.