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

  • Edge coloring


    We propose an algorithm for preventing race conditions in the evaluation of the surface integral contributions in edge-based CFD solvers by coloring the faces (or edges) of the computational mesh.

    Serial and multithreaded implementations for unstructured meshes of triangles and tetrahedra described in

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

    are available for download [here].

    The multithreaded implementations for triangles and tetrahedra can color 1 million elements/second on a standard laptop.

    Moment limiting for the discontinuous Galerkin method on unstructured meshes

    Codes to determine the interpolation elements and weights for the moment limiters described in

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

    are available for download [here].