Lilia Krivodonova

Associate Professor
Associate Chair, Graduate Studies
Department of Applied Mathematics
University of Waterloo

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

Finite element and discontinuous Galerkin methods

Adaptive computations

GPU computing

Musical Accoustics

Publications	Students	Images	Software

My Google Scholar profile

Fast non-uniform quadrilateral mesh generation.

Adaptive mesh refinement on graphics processing units for applications in gas dynamics.

pdf

A moment limiter for the discontinuous Galerkin method on unstructured triangular meshes.

pdf

A Robust CFL Condition for the Discontinuous Galerkin Method on Triangular Meshes.

pdf

On the optimal CFL number of SSP methods for hyperbolic problems.

pdf

Axisymmetric Simulations of Nonlinear Sound Propagation in a Trumpet. /cite> In: Kilgour D., Kunze H., Makarov R., Melnik R., Wang X. (eds) Recent Advances in Mathematical and Statistical Methods, pp. 229-238, 2018

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

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

N. Chalmers and L. Krivodonova. Spatial and Modal Superconvergence of the Discontinuous Galerkin Method for Linear Equations, Journal of Scientific Computing, Vol. 72 (1), 128-146, 2017 .
[ pdf ]

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.

J. Resch, L. Krivodonova and J. Vanderkooy. A Comparison Between Two and Three-Dimensional Simulations of Finite Amplitude Sound Waves in a Trumpet , Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 435-445, 2016.

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(12), 982-1003,2014.

N. Chalmers, L. Krivodonova, and R. Qin. Relaxing the CFL condition of the discontinuous Galerkin method, SIAM Journal on Scientific Computing, Vol. 36 (4), A2047-A2075, 2014.

J. Resch, L. Krivodonova and J. Vanderkooy. A Two-Dimensional Study of Finite Amplitude Sound Waves in a Trumpet Using the Discontinuous Galerkin Method, Journal of Computational Accoustics, Vol. 22(3), 2014.

D. Connor and L. Krivodonova. Interpolation of two-dimensional curves with Euler spirals, Journal of Applied and Computational Mathematics, Vol 261: 320-332, 2014.

L. Krivodonova and R. Qin. An analysis of the spectrum of the discontinuous Galerkin method II: Nonuniform grids , Applied Numerical Mathematics, Vol 71: 41-62, 2013.

L. Krivodonova and R. Qin. An analysis of the spectrum of the discontinuous Galerkin method, Applied Numerical Mathematics, Vol. 64:1-18, 2013.

R. Qin and L. Krivodonova. A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries , Journal of Computational Science, Vol. 4 (1-2), 24-35, 2013.

L. Krivodonova. An Efficient Local Time Stepping Scheme for Solution of Nonlinear Conservation Laws. J. of Comp. Physics, Vol. 229:8537-8551, 2010.

L. Krivodonova. Limiters for High-Order Discontinuous Galerkin Methods. J. of Comp. Physics, Vol. 226(1):276-296,2007.

L. Krivodonova and M. Berger. High-order Accurate Implementation of Solid Wall Boundary Conditions in Curved Geometries. J. of Comp. Physics, Vol. 211:492-512, 2006.

L. Krivodonova, J. Xin, J.-F. Remacle, N. Chevaugeon, and J.E. Flaherty. Shock Detection and Limiting with Discontinuous Galerkin Methods for Hyperbolic Conservation Laws. Applied Numerical Mathematics, Vol. 48:323-338, 2004.

L. Krivodonova and J. Flaherty. Error Estimation for Discontinuous Galerkin Solutions of Multidimensional Hyperbolic Problems. Advances in Computational Mathematics, Vol. 19:57-71, 2003.

J. Flaherty, L. Krivodonova, J.-F. Remacle, and M. Shephard. Aspects of Discontinuous Galerkin Methods for Hyperbolic Conservation Laws. Finite Elements in Analysis and Design, Vol. 38:889 - 908, 2002.

S. Adjerid, K. Devine, J. Flaherty, and L. Krivodonova. A Posteriori Error Estimation for Discontinuous Galerkin Solutions of Hyperbolic Problems. Computer Methods in Applied Mechanics and Engineering, Vol. 191:1097-1112, 2002.

Lilia Krivodonova lgk at uwaterloo.ca