Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908866202042368 |
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| author | Garai, Gobinda Chamakuri, Nagaiah |
| author_facet | Garai, Gobinda Chamakuri, Nagaiah |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04350 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs Garai, Gobinda Chamakuri, Nagaiah Numerical Analysis 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. |
| title | Exp-ParaDiag: Time-Parallel Exponential Integrators for Parabolic PDEs |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.04350 |