Francesco Patrizi (ESR8)

2016-Cur. PhD student, Univerisity of Oslo with external partner SINTEF.
2014-2016 Master’s degree in Pure and Applied Mathematics, University of Rome “Tor Vergata”.
Thesis: “A modified multigrid method for linear systems arising from isogeometric analysis”.
2009-2013 Bachelor’s degree in Mathematics, University of Rome “Tor Vergata”.

Research Activities:
2016-2017 Reviewer for Computer Aided Geometric Design, Elsevier.

Project: Refinement strategies and linear independence for LR-splines

Supervisor: Tor Dokken

Institution: Dept of Applied Mathematics, SINTEF, Oslo, Norway

Providing refinement strategies for LR-splines that ensure linear independence, numerical stability and the anticipated error reduction of LR-spline approximations.
In its general form, LR-splines are incredibly versatile: the only restriction in the refinement process is that at each step at least one B-spline is refined. Even so, experiments have shown that care has to be take to maintain linear independence and a numerically stable B-spline basis. Currently, this is managed through restrictive rules of thumb, such as avoiding overloaded elements or B-splines, and avoiding B-splines with nested support. Refinements are often restricted to the midpoint of knot intervals. This project will develop refinement strategies incorporating these informal rules. One of the challenges this project will address is how the choice of refinement direction can be optimised in order to maximise the approximation power of LR-splines. A second challenge is refinements strategies for big data, where typically the size of both the original data and of the approximate LR-spline model requires tiling into manageable pieces. Different application areas will typically require different refinement strategies. This will be incorporated into the project through the two secondment periods. At UoS, the focus will be on refinement strategies suitable for isogeometric analysis, i.e., for creating geometric models suitable both for design and simulation purposes. At Hue, the focus will be on adapting LR-spline algorithms for modelling and visualisation of very large seismic datasets. The development of a plugin for their HueSpace software platform will enable testing of the refinement strategies on complex real-world seismic workflows.The project will take place at the Dept of Applied Mathematics, SINTEF. The PhD will be awarded by the University of Oslo.

Secondments  are planned at U. Strathclyde (Glasgow, UK) and at industrial partner Hue (Oslo, Norway).