Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies

Gobinda Garai; Nagaiah Chamakuri

Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies

Numerical Analysis 2026-07-02 v1

Authors: Gobinda Garai , Nagaiah Chamakuri

Abstract

This paper presents a development of a nonlinear extension of the Parareal-Incomplete Optimized Schwarz Waveform Relaxation (OSWR) method, aimed at efficiently simulating coupled reaction-diffusion systems, with particular attention to those encountered in cardiac electrophysiology. The strategy leverages the synergy of spatial and temporal decomposition to tackle the computational challenges of large-scale, nonlinear simulations. The proposed approach is accompanied by a comprehensive convergence analysis. Extensive numerical experiments confirm the convergence of the nonlinear Parareal-Incomplete OSWR method. The results showcase its robust convergence behavior across various space-time subdomains, underscoring the method's reliability and effectiveness, especially in complex simulations involving multiple subdomains.

Keywords

Parareal optimized Schwarz waveform relaxation reaction-diffusion systems convergence analysis cardiac electrophysiology domain decomposition

Cite

@article{arxiv.2607.02780,
  title  = {Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies},
  author = {Gobinda Garai and Nagaiah Chamakuri},
  journal= {arXiv preprint arXiv:2607.02780},
  year   = {2026}
}