I am a PhD student in numerical analysis at the divison of scientific computing, and supervised by Maya Neytcheva and Gunilla Kreiss.

My main research project is about robust preconditioning methods for algebraic problems, arising in multi-phase flow models, see the project's webpage.
The aim of the project is to construct, analysis and implement fast and reliable numerical solution methods to simulate multi-phase flow, modeled by a coupled system consisting of the time-dependent Cahn-Hilliard and incompressible Navier-Stokes equations, aiming at constructing preconditioners, which are numerically and computationally efficient and robust with respect to various problem, discretization and method parameters.

1. M. Neytcheva, M. Do-Quang and X. He, Element-by-element Schur complement approximations for general nonsymmetric matrices of two-by-two block form. Springer Lecture Notes in Computer Science (LNCS), 5910/2010, 2010.

2. X. He, M. Neytcheva and S. Serra Capizzano, On an augmented Lagrangian-based preconditioning of Oseen type problems. Submitted to BIT Journal, and under revision now, 2010. PDF.

3. X. He and M. Neytcheva, Preconditioning the incompressible Navier-Stokes equations with variable viscosity. Technical Report, 2011-006, 2011. Department of Information Technology, Uppsala University, Sweden. PDF.

4. X. He, Robust preconditioning methods for algebraic problems, arising in multi-phase flow models. Licentiate thesis, 2011-002, 2011. Department of Information Technology, Uppsala University, Sweden. PDF.