Who I am
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.