Zhengfu Xu

Fisher Hall


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Associate Professor, Mathematical Sciences

  • PhD, Applied Mathematics, Brown University
  • MS, Computational Mathematics, Peking University
  • BS, Computational Mathematics, Peking University


Zhengfu received his B.Sc. and M. Sc in Mathematics from the Department of Mathematics at Peking University. Then he went on to the division of applied mathematics at Brown University for his graduate studies.  He got an M.Sc (minor in computer science) and PhD of applied mathematics from Brown University. After his graduation, he worked as the S Chowla research assistant professor in the department of mathematics at Penn State University. Before he moved to the Michigan Technological University, he worked as research assistant professor in the department of mathematics at Michigan State University. He is now an Assistant Professor at the Department of Mathematics in Michigan Technological University.

His research focuses on high order numerical methods for solving partial differential equation. His interest of research also includes inverse problems, mathematical imaging, nonlinear optics. His recent work is on computational modeling of the morphology of the nano-scaled network in the polymer electrolyte membrane (also known as proton exchange membrane) fuel cell.

He is a member of the Society for Industrial and Applied Mathematics.

Areas of Expertise

  • Numerical PDE, Scientific computing
  • Computational modeling of Nafion material
  • Mathematical image processing, inverse problems, nonlinear optics

Recent work:

  • T. Xiong, J.-M Qiu and Z. Xu, Parametrized positivity preserving flux limiters for high order finite difference WENO scheme solving compressible Euler equations, resubmitted after revision.
  • A. Christlieb, Y. Liu and Z. Xu, High order operator splitting methods based on an integral deferred correction framework, submitted.
  • T. Xiong, J. Qiu and Z. Xu, A maximum principle preserving limiter for discontinuous Galerkin method with applications to convection-diffusion equations, accepted by SIAM Journal on Scientific Computing after revision. Read More
  • R. Guo, Y. Xu, and Z. Xu, Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation, accepted by Journal of Scientific Computing.
  • L. Guo, J.-F. Jiang, Y. Xu, Z. Xu, A PDE-based regularization algorithm toward reducing speckle tracking noise: A feasibility study for ultrasound breast elastography, accepted by Ultrasonic Imaging.
  • A. Christlieb, Y. Liu, Q. Tang and Z. Xu, Parametrized Maximum-principle-preserving and positivity-preserving flux limiter for WENO schemes on unstructured meshes, Journal of Computational Physics, 281(15) (2015), 334--351.
  • T, Xiong, J.-M. Qiu, A. Christlieb and Z. Xu, High order maximum principle preserving semi-Lagrangian finite difference WENO schemes for the Vlasov equation, Journal of Computational Physics, 273 (2014), 618--639.
  • Y. Jiang, Z. Xu, Parametrized maximum principle preserving limiter for finite difference WENO schemes solving convection-dominated diffusion equations, SIAM Journal on Scientific Computing, 35(6) (2013), 2524– 2553. Read More
  • T. Xiong, J.-M Qiu and Z. Xu, A parametrized maximum principle preserving flux limiter for finite difference RK-WENO schemes with applications in incompressible flows, Journal of Computational Physics, 252 (2013), 310–331.
  • C. Liang, Z. Xu, Parametrized maximum principle preserving flux limiters for high order schemes solving multi-dimensional scalar hyperbolic conservation laws, Journal of Scientific Computing, 58 (2014), 41–60. Read More
  • Z. Xu, Parametrized maximum principle preserving flux limiters for high order schemes solving hyperbolic conservation laws: one-dimensional scalar problem, Mathematics of Computation, 83 (2014), 2213--2238. Read More
  • Z. Xu, A. Christlieb and K. Promislow, On the nonlinear unconditionally gradient scheme for Cahn-Hilliard equation and its implementation with Fourier method, Communications in Mathematical Sciences, 11(2)(2013), 345–360.
  • N. Gavish, J. Jones, Z. Xu, A. Christlieb, and K. Promislow, Variational Models of Network Formation and Ion Transport: Applications to Ionomer Membranes, Polymers, 4(1) (2012), 630–655.
  • Sole PI, NSF grant- DMS-1316662 “High Order Maximum Principle Preserving Finite Difference Schemes for Hyperbolic Conservation Laws,” in the amount of $226,349, 2013–2016.