High-order discontinuous Galerkin methods for the monodomain and bidomain models
This work aims at presenting a discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated by the characteristic of the mathematical solution of such e...
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| Language: | English |
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AIMS Press
2024-12-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2024028 |
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| author | Federica Botta Matteo Calafà Pasquale C. Africa Christian Vergara Paola F. Antonietti |
| author_facet | Federica Botta Matteo Calafà Pasquale C. Africa Christian Vergara Paola F. Antonietti |
| author_sort | Federica Botta |
| collection | DOAJ |
| description | This work aims at presenting a discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated by the characteristic of the mathematical solution of such equations which often corresponds to a highly steep wavefront. Hence, the built-in flexibility of discontinuous methods in developing adaptive approaches, combined with the high-order accuracy, can well represent the underlying physics. The choice of a semi-implicit time integration allows for a fast solution at each time step. The article includes some numerical tests to verify the convergence properties and the physiological behaviour of the numerical solution. Also, a pseudo-realistic simulation turns out to fully reconstruct the propagation of the electric potential, comprising the phases of depolarization and repolarization, by overcoming the typical issues related to the steepness of the wave front. |
| format | Article |
| id | doaj-art-0cc6a1e5dd3148869d3f58d3a5b40870 |
| institution | Kabale University |
| issn | 2640-3501 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj-art-0cc6a1e5dd3148869d3f58d3a5b408702025-01-24T01:08:41ZengAIMS PressMathematics in Engineering2640-35012024-12-016672674110.3934/mine.2024028High-order discontinuous Galerkin methods for the monodomain and bidomain modelsFederica Botta0Matteo Calafà1https://orcid.org/0009-0007-4426-7240Pasquale C. Africa2https://orcid.org/0000-0002-0706-8564Christian Vergara3https://orcid.org/0000-0001-9872-5410Paola F. Antonietti4https://orcid.org/0000-0002-2138-3878Independent researcher; federica.botta@mail.polimi.itDepartment of Mechanical and Production Engineering, Aarhus University, Katrinebjergvej 89F, Aarhus 8200, DenmarkmathLab, SISSA, via Bonomea, 265, Trieste 34136, ItalyLABS, Dipartimento di Chimica, Materiali e Ingegneria Chimica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, ItalyMOX, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano 20133, ItalyThis work aims at presenting a discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated by the characteristic of the mathematical solution of such equations which often corresponds to a highly steep wavefront. Hence, the built-in flexibility of discontinuous methods in developing adaptive approaches, combined with the high-order accuracy, can well represent the underlying physics. The choice of a semi-implicit time integration allows for a fast solution at each time step. The article includes some numerical tests to verify the convergence properties and the physiological behaviour of the numerical solution. Also, a pseudo-realistic simulation turns out to fully reconstruct the propagation of the electric potential, comprising the phases of depolarization and repolarization, by overcoming the typical issues related to the steepness of the wave front.https://www.aimspress.com/article/doi/10.3934/mine.2024028discontinuous galerkin methodselectrophysiologyspectral methodscardiac modellingreaction-diffusion equations |
| spellingShingle | Federica Botta Matteo Calafà Pasquale C. Africa Christian Vergara Paola F. Antonietti High-order discontinuous Galerkin methods for the monodomain and bidomain models Mathematics in Engineering discontinuous galerkin methods electrophysiology spectral methods cardiac modelling reaction-diffusion equations |
| title | High-order discontinuous Galerkin methods for the monodomain and bidomain models |
| title_full | High-order discontinuous Galerkin methods for the monodomain and bidomain models |
| title_fullStr | High-order discontinuous Galerkin methods for the monodomain and bidomain models |
| title_full_unstemmed | High-order discontinuous Galerkin methods for the monodomain and bidomain models |
| title_short | High-order discontinuous Galerkin methods for the monodomain and bidomain models |
| title_sort | high order discontinuous galerkin methods for the monodomain and bidomain models |
| topic | discontinuous galerkin methods electrophysiology spectral methods cardiac modelling reaction-diffusion equations |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2024028 |
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