Weizhu Bao


I have conducted research in Bose-Einstein condensation; computational fluid dynamics; computational quantum physics and chemistry; hyperbolic conservation laws; multiscale modeling, simulation and applications; quantized vortices in superfluidity and superconductivity; numerical methods for problems in unbounded domains; finite element method for some nonlinear problems; numerical analysis and scientific computing; computational and applied mathematics in general.

Multiscale Methods and Analysis for Oscillatory PDEs


For Klein-Gordon and Dirac equations (nonrelativistic limit)

For nonlinear Schrodinger equation (semiclassical limit)

For Zakharov system (subsonic limit)

For coupled dispersive PDEs


Modeling and Simulation for Solid-State Deweeting Problems


Triple junction drag effects during topological changes in the evolution of polycrystalline microstructures (with Q. Zhao, W. Jiang and D. J. Srolovitz), Acta Mater., to appear (arXiv: 1611.09449).

Stable equilibria of anisotropic particles on substrates: a generalized Winterbottom construction (with W. Jiang, D. J. Srolovitz and Y. Wang), arXiv: 1608.08481.

A parametric finite element method for solid-state dewetting problems with anisotropic surface energies (with W. Jiang, Y. Wang and Q. Zhao), J. Comput. Phys., Vol. 330 (2017), pp. 380-400 (arXiv: 1601.05877).

Solid-state dewetting and island morphologies in strongly anisotropic materials (with W. Jiang, Y. Wang, Q. Zhao, D. J. Srolovitz), Scripta Materialia, Vol. 115 (2016), pp. 123-127 (arXiv: 1510.03303).

Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energy (with W. Jiang, D. J. Srolovitz, Y. Wang), Phys. Rev. B, Vol. 91 (2015), article 045303.

Phase field approach for simulating solid-state dewetting problems (with W. Jiang, C. V. Thompson and D. J. Srolovitz), Acta Mater., Vol. 60 (2012), pp. 5578-5592.


Bose-Einstein Condensation (BEC)


Review Papers

For single-component BEC

For rotating BEC

For dipolar BEC

For spinor and multi-component BEC

For polariton condensate


Quantized Vortex in Superfluidity and Superconductivity


The kinematic effects of the defects in liquid crystal dynamics (with X. Zhao), Commun. Comput. Phys., Vol. 20 (2016), pp. 234-249.

Numerical study of quantized vortex interaction in nonlinear Schroedinger equation on bounded domains (with Q. Tang), Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 12 (2014), pp. 411-439.

Numerical study of quantized vortex interaction in the Ginzburg-Landau equation on bounded domains (with Q. Tang), Commun. Comput. Phys., Vol. 14 (2013), pp. 819-850.

Quantized vortex stability and interaction in the nonlinear wave equation (with R. Zeng and Y. Zhang), Physica D, Vol. 237 (2008), pp. 2391-2410.

The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schrodinger equations (with Q. Du and Y. Zhang), SIAM J. Appl. Math., Vol. 67 (2007), pp. 1740-1775.

Dynamics of vortices in weakly interacting Bose-Einstein condensates (with A. Klein, D. Jaksch and Y. Zhang), Phys. Rev. A, Vol. 76 (2007), article 043602.

Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation (with Q. Du and Y. Zhang), Eur. J. Appl. Math., Vol. 18 (2007), pp. 607-630.


Artificial Boundary Conditions and Error Estimates


For incompressible flow

For linear elasticity and incompressile materials

For elliptic problems


Computational Fluid Dynamics


High-order I-stable central difference schemes for viscous compressible flows (with J. Shi), J. Comput. Math., Vol. 21 (2003), pp. 101-112.

Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms (with S. Jin), Appl. Numer. Math., Vol. 43 (2002), pp. 315-333.

An economical finite element approximation of a generalized Newtonian flow , Comput. Methods Appl. Mech. Engrg., Vol. 191 (2002), pp. 3637-3648.

The random projection method for stiff multi-species detonation capturing (with S. Jin), J. Comput. Phys., Vol. 178 (2002), pp. 37-57.

The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23 (2001), pp. 1000-1026.

On inf-sup conditions of mixed finite element formulations for acoustic fluids (with X. Wang and K. J. Bathe), Math. Mod. Meth. Appl. Sci., Vol. 11 (2001), pp. 883-901.

Weakly compressible high-order I-stable central difference schemes for incompressible viscous flows (with S. Jin), Comput. Methods Appl. Mech. Engrg., Vol. 190 (2001), pp. 5009-5026.

The random projection method for hyperbolic systems with stiff reaction terms (with S. Jin), J. Comput. Phys., Vol. 163 (2000), pp. 216-248.

A priori and posteriori error bounds for nonconforming linear finite element approximation of a non-Newtonian flow (with J. W. Barrett), M^2AN Math. Model. Numer. Anal., Vol. 32 (1998), pp. 843-858.


Miscelansous


Single-polymer `flyfishing' effect for nanoscale motors and machines: an exact worm-like-chain model study (with N. Wang, R. Hou and Z. Wang), arXiv: .

A variational-difference numerical method for designing progressive-addition lenses (with W. Jiang, Q. Tang and H. Wang), Computer-Aided Design, Vol. 48 (2014), pp. 17-27.

Approximation and comparison for motion by mean curvature with intersection points , Computers & Math. Appl. , Vol. 46 (2003), pp. 1211-1228.