PDRA in Computational Stochastics working with Michael B. Giles (Oxford).
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Deflation for semismooth equations
Optimization Methods and Software (16 May 2019)
Efficient white noise sampling and coupling for multilevel Monte Carlo
with non-nested meshes
SIAM/ASA Journal on Uncertainty Quantification issue 4 volume 6 page 1630-1655 (20 November 2018)
Complexity bounds on supermesh construction for quasi-uniform meshes
Journal of Computational Physics
Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields
Fluids and Barriers of the CNS issue 2019 volume 16 page 32- (30 September 2019)
Fast uncertainty quantification of tracer distribution in the brain
interstitial fluid with multilevel and quasi Monte Carlo
Full text available
Multilevel quasi Monte Carlo methods for elliptic PDEs with random field
coefficients via fast white noise sampling
Full text available
The main focus of my research is on multilevel Monte Carlo and finite element methods for the solution of PDEs with random coefficients and spatial white noise driven SPDEs. Currently, the application in mind is the quantification of uncertainty in brain fluid simulation.
Main research interests:
- Low-precision numerical solvers for PDEs
- Finite Element Methods for PDEs
- Multilevel Monte Carlo and Multilevel Quasi Monte Carlo
- Numerical Methods for Spatial White Noise driven SPDEs
- PDEs with Random Coefficients
- Uncertainty Quantification for SPDEs
- Mathematical Modelling of the Brain Physiology
- Numerical Linear Algebra
- Deflation for Complementarity Problems
Lay-man description of my DPhil thesis work.
FEniCS-based multilevel (quasi) Monte Carlo software for PDEs with random coefficients here.
Prizes, awards, and scholarships:
2015-2019: Oxford-Radcliffe Scholarship
Major / recent publications:
M. Croci, M. B. Giles, M. E. Rognes, P. E. Farrell - Multilevel quasi Monte Carlo methods for elliptic PDEs with random field coefficients via fast white noise sampling - submitted to SISC - preprint.
M. Croci, P. E. Farrell - Complexity bounds on supermesh construction for quasi-uniform meshes - Journal of Computational Physics - preprint.
M. Croci, V. Vinje and M. E. Rognes - Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo - submitted to International Journal for Numerical Methods in Biomedical Engineering.