LocalROM

MATLAB(R) scripts for the numerical approximation of the Fitzhugh-Nagumo membrane model using local reduced-order models.

LocalROM has been developed at MOX-Politecnico di Milano under the support of the ERC Advanced Grant iHEART project. It includes straightforward implementations of the local reduced-order models presented in the submitted article:

[[PMQ18] S. Pagani, A. Manzoni, A. Quarteroni. Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method, Computer Methods in Applied Mechanics and Engineering, 340, 530–558, 2018.]

Download and Installation

To install the library, extract the ZIP file or clone the git repository.

Run the script by running the setup file

setPath

Examples

• FOM: numerical approximation of the parametrized Fitzhugh-Nagumo membrane model for an instance of the parameter epsilon.

• GlobalROMConvergence: mean relative error convergence analysis with respect to the number of POD basis functions for the global reduced-order model.

• GlobalROMHyperred: mean relative error convergence analysis with respect to the number of POD basis functions for the global hyperreduced model.

• LocalROM: mean relative error convergence analysis with respect to the number of POD basis functions for the local reduced-order models (time-, parameter- and state-based).

• LocalROMHyperred: mean relative error convergence analysis with respect to the number of POD basis functions for the local hyperreduced models (time-, parameter- and state-based).

License

Freely available subject to a BSD 2-Clause License.
Please cite this code by adding the following reference to your work:

[[PMQ18] S. Pagani, A. Manzoni, A. Quarteroni. Numerical approximation of parametrized problems in cardiac electrophysiology by a local reduced basis method, Computer Methods in Applied Mechanics and Engineering, 340, 530–558, 2018.]

Development

LocalROM was developed and is currently maintained by Stefano Pagani.