An agglomeration-based multigrid solver for the discontinuous Galerkin discretization of cardiac electrophysiology

[2602.16312] An agglomeration-based multigrid solver for the discontinuous Galerkin discretization of cardiac electrophysiology Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2602.16312 (math) [Submitted on 18 Feb 2026 ( v1 ), last revised 16 Jul 2026 (this version, v4)] Title: An agglomeration-based multigrid solver for the discontinuous Galerkin discretization of cardiac electrophysiology Authors: Marco Feder , Pasquale Claudio Africa View PDF HTML (experimental) Abstract: This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in cardiac electrophysiology. The proposed approach exploits general polytopic grids at coarser levels, obtained through the agglomeration of elements from an initial, potentially fine, mesh. By leveraging a robust and efficient agglomeration strategy, we construct a nested hierarchy of grids suitable for multilevel solver frameworks. The effectiveness and performance of the methodology are assessed through a series of numerical experiments on two- and three-dimensional domains, involving different ionic models and realistic unstructured geometries. The results demonstrate strong solver effectiveness and favorable scalability with respect to both the polynomial degree of the discretization and the number of levels selected in the multigrid preconditioner. Subjects: Numerical Analysis (math.NA) Cite as: arXiv:2602.16312 [math.NA] (or arXiv:2602.16312v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2602.16312 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Computer Methods in Applied Mechanics and Engineering. 462 (2026), 119298 Related DOI : https://doi.org/10.1016/j.cma.2026.119298 Focus to learn more DOI(s) linking to related resources Submission history From: Pasquale Claudio Africa [ view email ] [v1] Wed, 18 Feb 2026 09:47:20 UTC (3,675 KB) [v2] Mon, 4 May 2026 08:03:03 UTC (6,379 KB) [v3] Mon, 15 Jun 2026 22:01:55 UTC (6,387 KB) [v4] Thu, 16 Jul 2026 07:58:27 UTC (6,387 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-02 Change to browse by: cs cs.NA math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• An agglomeration-based multigrid solver for the discontinuous Galerkin discretization of cardiac electrophysiology#674301
• Development of discontinuous galerkin method 2 dimensional flow solver#646228
• MATHICSE Technical Report : A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations#308396
• A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs#781148
• A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs#779773