D.Phil. in EPSRC Centre for Doctoral Training in Partial Differential Equations
Supervisor: Patrick E. Farrell
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Nonlinear bifurcation analysis of stiffener profiles via deflation techniques
Thin Walled Structures issue April 2020 volume 149 (17 February 2020)
Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrodinger Equations
COMMUNICATIONS IN COMPUTATIONAL PHYSICS issue 4 volume 25 page 1127-1143 (April 2019) Full text available
- Numerical solutions to PDEs.
- Bifurcation Analysis of nonlinear PDEs
- Liquid crystal problems (Oseen--Frank models)
Currently, I am working on developing robust and efficient solvers for a nonlinear constrained optimization problem deriving from Liquid Crystals with preconditioning techniques. During such processes, I am looking for contructing a robust multigrid algorithm and using augmented Lagrangian methods as potential effective preconditioners.
Michaelmas Term 2019:
B6.1 Numerical Solution of Differential Equations I
Hilary Term 2020:
B6.2 Numerical Solution of Differential Equations II
Major / recent publications:
Nonlinear Bifurcation Analysis of Stiffener Profiles via Deflation Techniques
J. Xia; P. E. Farrell; S. G. P. Saullo. 2020, Thin-Walled Structures.