Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs
Abstract
This paper introduces Exp-ParaDiag, a novel time-parallel method that combines the strength of exponential integrators into the ParaDiag framework. We develop and analyze Exp-ParaDiag based on first and second order accurate exponential integrators. We establish the convergence of the proposed methods both as preconditioned fixed-point iterations and as precon- ditioners within the GMRES framework. Furthermore, we extend the Exp-ParaDiag formulation to achieve sixth-order temporal accuracy using exponential integrators. The proposed approach is also generalized to nonlinear problems, for which convergence is rigorously demonstrated. A series of numerical experiments is presented to validate the theoretical results and to illustrate the robustness and efficiency of the developed methods.
Cite
@article{arxiv.2603.04350,
title = {Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs},
author = {Gobinda Garai and Nagaiah Chamakuri},
journal= {arXiv preprint arXiv:2603.04350},
year = {2026}
}