Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs

Gobinda Garai; Nagaiah Chamakuri

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arXiv · 2603.04350

Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs

Gobinda Garai·Nagaiah Chamakuri

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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.

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BibTeX RIS

Gobinda Garai, Nagaiah Chamakuri. 2026-03-04. Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs. https://arxiv.org/abs/2603.04350

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