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arXiv · 2607.02780

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

Gobinda Garai·Nagaiah Chamakuri
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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.

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Gobinda Garai, Nagaiah Chamakuri. 2026-07-02. Nonlinear Parareal-Incomplete OSWR Method for the Coupled Reaction-Diffusion System: Convergence Analysis and Computational Strategies. https://arxiv.org/abs/2607.02780

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