Numerical Analysis Group's Graduate Student Coordinator
+44 1865 615121
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
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)
Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields
Fluids and Barriers of the CNS
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. The application in mind is the quantification of uncertainty in brain fluid simulation.
Main research interests:
- 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.
I am a fourth year DPhil student in Cohort 2 of the EPSRC CDT in Industrially Focused Mathematical Modelling working with Patrick E. Farrell (Oxford), Michael B. Giles (Oxford) and Marie E. Rognes (Simula Research Laboratory).
Prizes, awards, and scholarships:
2015-2019: Oxford-Radcliffe Scholarship
Major / recent publications:
M. Croci, V. Vinje, M. E. Rognes - Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields - to appear in Fluids and Barriers of the CNS - Preprint.
M. Croci, M. B. Giles, M. E. Rognes, P. E. Farrell - Multilevel quasi Monte Carlo methods for elliptic partial differential equations driven by spatial white noise - in preparation.