12 papers
A stability-preserving polytopal discontinuous Galerkin method for the Fisher-Kolmogorov model with applications to neurodegenerative disease modelling
Paola Francesca Antonietti, Francesca Bonizzoni, Mattia Corti +3
The Fisher--Kolmogorov equation models the spatio-temporal evolution of interacting biological species and is extensively employed in fields such as ecology, population dynamics, a…
A whole-brain model of amyloid beta accumulation and cerebral hypoperfusion in Alzheimer's disease
Mattia Corti, Andrew Ahern, Alain Goriely +2
Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and…
The lymph 2.0 library: p-adaptive algorithms and parallel assembly strategies for polytopal DG methods
Paola F. Antonietti, Mattia Corti, Caterina B. Leimer Saglio +1
This work presents a new release of the lymph 2.0 library, an open-source MATLAB framework for high-order discontinuous Galerkin discretizations on general polytopal meshes. The ly…
On the Compact Discontinuous Galerkin method for polytopal meshes
Mattia Corti, Sergio Gómez
The Compact Discontinuous Galerkin method was introduced by Peraire and Persson in (SIAM J. Sci. Comput., 30, 1806-1824, 2008). In this work, we present the stability and convergen…
Optimized high-order IMEX-RK schemes for degenerate diffusion-reaction problems with application to travelling waves phenomena
Paola F. Antonietti, Mattia Corti, Giuseppe Orlando
We study a class of IMplicit-EXplicit Runge--Kutta (IMEX-RK) schemes for the numerical approximation of reaction and diffusion-reaction problems arising in a variety of biological…
Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems
Paola F. Antonietti, Mattia Corti, Sergio Gómez +1
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretiza…