Assistant Professor/Courant Instructor
Courant Institute of Mathematical Sciences
New York University

The main focus of my research is adaptive, high-order, parallel methods for solution of partial differential equations.

  • Finite element and discontinuous Galerkin methods
  • GPU computing
  • Mesh generation
  • Adaptive computations

  • Refereed Articles

    A. Giuliani and L. Krivodonova. A moment limiter for the discontinuous Galerkin method on unstructured triangular meshes. SIAM Journal on Scientific Computing. Vol. 41(1):A508-A537, 2019. [ preprint ]

    A. Giuliani and L. Krivodonova. Adaptive mesh refinement on graphics processing units for applications in gas dynamics. Journal of Computational Physics. Vol. 381:67-90, 2019. [ preprint ]

    A. Giuliani and L. Krivodonova. On the optimal CFL number of SSP methods for hyperbolic problems. Applied Numerical Mathematics, Vol. 135, pp. 165-172, 2019. [ preprint ]

    A. Giuliani and L. Krivodonova. Analysis of slope limiters on unstructured triangular meshes. Journal of Computational Physics, Vol. 374:1–26, 2018. [ preprint ]

    A. Giuliani and L. Krivodonova. Face coloring in unstructured CFD codes, Parallel Computing, Vol. 63:17-37, 2017, 2017. [ preprint ]

    N. Voeltzel, A. Giuliani, N. Fillot, P. Vergne, and L. Joly. Nanolubrication by ionic liquids: molecular dynamics simulations reveal an anomalous effective rheology, Physical Chemistry Chemical Physics, Vol. 17:23226-23235, 2015.

    M. Fuhry, A. Giuliani and L. Krivodonova. Discontinuous Galerkin methods on graphics processing units for nonlinear hyperbolic conservation laws, International Journal for Numerical Methods in Fluids, Vol. 76:982-1003, 2014. [ preprint ]

    Conference Proceedings

    J. Resch, A. Giuliani, L. Krivodonova, and J. Vanderkooy. A comparison between axisymmetric and three-dimensional simulations of nonlinear sound propagation in a trumpet.

    A. Giuliani and L. Krivodonova. An h-Adaptive Implementation of the Discontinuous Galerkin Method for Nonlinear Hyperbolic Conservation Laws on Unstructured Meshes for Graphics Processing Units, Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 435-445, 2016.

    Thesis

    A. Giuliani A parallel, adaptive discontinuous Galerkin method for hyperbolic problems on unstructured meshes. Accepted August 2018 [ PDF ]

    Submitted Manuscripts

    A. Giuliani and L. Krivodonova. A moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshes. [ draft ]

    A. Giuliani and L. Krivodonova. Fast non-uniform quadrilateral mesh generation. [ draft ]

    K. Dutt, A. Giuliani , and L. Krivodonova. An angular momentum conserving moment limiter for the discontinuous Galerkin method on unstructured triangular meshes.