Speaker
Description
Traveling wave phenomena are central in many biological processes, including electrical activity in neural and cardiac tissues. Their simulation is challenging due to sharp, fast-moving wavefronts that demand high spatial and temporal resolution, resulting in high computational costs.
Brain electrophysiology at the tissue level is a key example: the transmembrane potential exhibits steep wavefronts propagating along preferential axonal directions. Modeling these dynamics involves multiple scales and complex, anisotropic domains. We employ a high-order discontinuous Galerkin method on polygonal meshes (PolyDG) that remains computationally demanding. To address this, we propose a p-adaptive algorithm that exploits the localized nature of traveling waves: strong variations are confined to small regions, while the rest of the domain is nearly stationary. We design a posteriori error indicators to detect wavefronts and locally adjust the polynomial degree. Numerical results show that the method accurately captures wave dynamics and effectively simulates epileptic events in heterogeneous brain tissues, reducing degrees of freedom and computational cost while preserving high-order accuracy.
Bibliography
References:
@article{leimer_saglio_high-order_2024,
title = {A high-order discontinuous Galerkin method for the numerical modeling of epileptic seizures},
journal = {Computers \& Mathematics with Applications},
volume = {205},
pages = {112-131},
year = {2026},
issn = {0898-1221},
author = {Caterina B. {Leimer Saglio} and Stefano Pagani and Mattia Corti and Paola F. Antonietti}
}
@article{leimer_saglio_p-adaptive_2025,
title = {A p-adaptive polytopal discontinuous {G}alerkin method for high-order approximation of brain electrophysiology},
author = {Leimer Saglio, Caterina Beatrice and Pagani, Stefano and Antonietti, Paola F.},
journal = {Computer Methods in Applied Mechanics and Engineering},
year = {2025},
volume = {446},
pages = {118249},
}
@article{schreiner_simulating_2022,
title = {Simulating epileptic seizures using the bidomain model},
author = {Schreiner, Jakob and Mardal, Kent-Andre},
journal = {Scientific Reports},
year = {2022},
volume = {12},
number = {1},
pages = {10065},
}
