Programming

Biomedical modeling

Computational Fluid Dynamics

Navier-Stokes benchmark FreeFem code to validate and benchmark an unsteady NS solver.
Dropipe FreeFem code to validate pressure drop in CFD simulation.
- 2d version
- 3d version
Cerebral Venous Network FreeFem and Python codes to pre-process raw data from medical acquisitions, simulate the venous blood flow and post-process results [2].
.
2D Bifurcation sandbox problem; [currently private] FreeFem and Octave of 2D vascular toy problem.
Windkessel BC for FreeFEM .idp file to build implicit Windkessel BC matrices in FreeFEM [4].
- 2d version
- 3d version

Physiological modeling

Windkessel 0d Standalone Python code to test different Windkessel configurations.
Flow rate manager Octave module to process and resample flow rate acquisition.
Center lines; [currently private] Octave module to load, display and manage center line from vessel networks.

Diffusion based problems

Eye ball model Standalone Python project to run heat diffusion simulation in human eye ball, problem proposed and studied in [3].
2d brain NIRS Standalone Python project to run light propagation simulation in real-life brain 2d geometry, problem proposed and studied in [1].
Simplified NIRS Standalone Python project to run light propagation simulation in simplified mutli-layer brain geometry, problem proposed and studied in [5].

Reduced Order Modeling

Reduced Basis Methods

Proper Orthogonal Decomposition modules to run POD on data sets, with test certification.
Reduced Basis Suite FreeFem code to manage RB items [WiP].
Old Reduced Basis Code FreeFem code to run Reduced Basis Method problems [depreciated].

Associated modules

Empirical Interpolation Method code to perform EIM on data set.
Parametrized-Background Data-Weak code to run PBDW state estimations [WiP].

Data assimilation

Linear state estimation

[WiP]

Ensemble Methods

Ensemble Kalman Method Method to solve parameter estimation problems
- Octave/Matlab(c) module
- [Python] [WiP]
Ensemble Kalman Filter [WiP]

Numerical Analysis

Radial Basis Function; Octave module to perform RBF interpolation with several kernel functions.
Non-Parametric Estimation [WiP]

Other numerical models

2d Graetz problem Standalone Python code to run 2d Graetz problem described in [7].
Thermal bloc problem Standalone Python code to run thermal bloc problem described in [6].

Miscellaneous

Freefem utils

Extended Linear Algebra FreeFem FreeFem code to perform standard LA operations between arrays and matrices.
FF Matlib FreeFem/Octave module to interface data structures. (forked project, original here).
FF Python FreeFem/Python code to interface data structures [WiP].

Other

Statistical Display Matlab Matlab(c) code to display distributed data over several categories.
Grid Manager Octave/Matlab(c) codes to manage 2D grid in 3D environment. Useful step to provide in silico MRI measurements.
Python Package template handy template to build Python package.

References

[1] B. Sulis, “Analyse multimodale et problèmes inverses pour l’imagerie cérébrale.,” These de doctorat, Reims, 2024. Available: https://theses.fr/2024REIMS006
[2] P. Mollo, G. Dollé, S. Salmon, and O. Balédent, “Accurate Cerebral Venous Blood Flow Simulations Compared to Real Data,” Apr. 2024. doi: 10.5281/zenodo.11032278.
[3] T. Saigre, C. Prud’homme, and M. Szopos, “Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball”, International Journal for Numerical Methods in Biomedical Engineering, vol. 40, no. 11, p. e3864, 2024, doi: 10.1002/cnm.3864.
[4] P. Mollo, “Coupling 2D/3D fluid models with 0D Windkessel model via boundary condition,” Oct. 2023. Available: https://hal.science/hal-04247891
[5] F. Oumri, “Modélisation mathématique, simulation numérique et application en tomographie optique chez l’enfant prématuré,” These de doctorat, Reims, 2021. Available: https://www.theses.fr/2021REIMS003
[6] N. Aretz-Nellesen, M. A. Grepl, and K. Veroy, “3D-VAR for Parametrized Partial Differential Equations: A Certified Reduced Basis Approach,” May 14, 2019, arXiv: arXiv:1905.05817. doi: 10.48550/arXiv.1905.05817.
[7] J. S. Hesthaven, G. Rozza, and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. in SpringerBriefs in Mathematics. Cham: Springer International Publishing, 2016. doi: 10.1007/978-3-319-22470-1.

Pierre Mollo

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