Choose a Section

Local links


UQ, Sensitivty Analysis, Machine Learning

  • Efficient computation of Sobol' indices for stochastic models, with J. Hart and A. Alexanderian, submitted.
  • Variable importance for scattered data, with J. Hart, submitted.
  • Methods of distributions for uncertainty quantification, with D. Tartakovsky, Handbook of Uncertainty Quantification, R. Ghanem, D. Higdon and H. Owadhi (Eds.), Springer, 2016, PDF.

Cardiovascular modeling

  • Classification of syncope through data analytics, with J. Hart, J. Mehlsen, C. Olsen, M.S. Olfusen, submitted.
  • Transcranial Doppler-based surrogates for cerebral blood flow: a statistical study, with J. Hart, V. Novak, C. Saunders, submitted.
  • Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model, with D. Guan and F. Liang, J. Biomechanics, 49 (2016), pp.1583--1592.
  • Impedance boundary conditions for general transient hemodynamics, with W. Cousins, Int. J. Numer. Biomed. Eng., 30 (2014), pp.1294--1313.
  • A new physiological boundary condition for hemodynamics, with W. Cousins and D.M. Tartakovsky, SIAM J. Appl. Math., 73 (2013), pp.1203--1223.
  • Boundary conditions for hemodynamics: the structured tree revisited, with W. Cousins, J. Comput. Phys., 231 (2012), pp.6086--6096.
  • Modeling cerebral blood flow and regulation, with M.C. Aoi, H.T. Tran, V. Novak and M. Olufsen, Eng. Med. Biol. Soc., 2009, pp.2410--2413.
  • Blood flow in the Circle of Willis: modeling and calibration, with K. DeVault, V. Novak, M.S. Olufsen, G. Vernieres and P.Zhao, Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, 27 (2008), pp.888--909.

Fluids, gas and transport

  • Analysis of a domain decomposition method for linear transport problems on networks, with J. Collins, Appl. Num. Math., 109 (2016), pp.61--72.
  • Numerical study of singularity formation in relativistic Euler flows, with Yi Sun, Comm. Comput. Phys., 16 (2014), pp.348--364.
  • Numerical Investigation of Cavitation in Multi-dimensional Compressible Flows, with K.J. DeVault and H.K. Jenssen, SIAM J. Appl. Math., 67 (2007), pp.1675-1692.
  • On a Penalty Method for the Navier-Stokes Problem in Regions with Moving Boundaries, with G. Amiez, Mat. Aplic. Com., 12 (1993), p.113--123.

Hamilton-Jacobi, free boundary, phase transition

  • Fast numerical methods for Bernoulli free boundary problems, with C.M. Kuster and R. Touzani, SIAM J. Sci. Comput., 29 (2007), pp.622-634.
  • A Study of Numerical Methods for the Level Set Approach, with C.M. Kuster and Zhilin Li, Applied Numerical Mathematics, 57 (2007), pp.837-846.
  • Computational Study of Fast Methods for the Eikonal Equation, with C.M. Kuster, SIAM J. Sc. Comp., 27 (2006), p.1803-1816.
  • Computation of Nonclassical Solutions to Hamilton-Jacobi Equations, with N. Ide, SIAM J. Sci. Comput., 21 (1999), p.502-521.
  • Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions, SIAM J. Numer. Anal., 31 (1994), p.111--127.
  • On an Elliptic-Parabolic Problem Related to Phase Transitions in Shape Memory Alloys, Numer. Funct. Anal. Opt., 14 (1993), p.355--370.
  • On a Numerical Approach to Stefan Like Problems, with G. Amiez, Numer.Math, 59 (1991), p.71--89.

Granular materials

  • Granular free surfaces, with Rachael Gordon-Wright, SIAM Rev., 55 (2013), pp.168--184.
  • Accurately Computing the Shape of Sandpiles, with C.M. Kuster, in Multiscale and Optimization Methods and Applications, Editors: W.W. Hager, S.J. Huang, P.M. Pardalos, O.A. Prokopyev, Nonconvex Optimization and its Applications, vol. 82, Springer, 2006, p.305-312.
  • On the Computation of Steady Hopper Flows III: Model Comparisons, with J.V. Matthews and D.G. Schaeffer, J. Comp. Phys., 219 (2006), p.443-454.
  • On the Computation of Steady Hopper Flows II: von Mises Materials in Various Geometries, with J.V. Matthews and M. O'Malley, J. Comput. Phys., 200 (2004), p.639-653.
  • Volume Determination for Bulk Materials in Bunkers, with S.A. Ahmed, R. Buckingham, C.D. Hauck, C.M. Kuster, M.Prodanovic, T.A. Royal and V. Silantyev, Int. J. Numer. Meth., 61 (2004), p.2239--2249.
  • Numerical Issues in Plasticity Models for Granular Flows, J. Volcanolgy and Geothermal Res., 139 (2005), p.23-31,
  • Secondary Circulation in Granular Flows through Axisymmetric Hoppers, with J.V. Matthews and D.G. Schaeffer, SIAM J. Appl. Math., 64 (2003), p.583-600.
  • Numerical Simulation of Aerated Powder Consolidation, with K.A. Coffey, Int. J. Nonlinear Mech., 38 (2003), p.1185-1194.
  • On a Powder Consolidation Problem, with C.T. Kelley, T.A. Royal and K.A. Coffey, SIAM J. Appl. Math., 62 (2001), pp.1-20.
  • On the Computation of Steady Hopper Flows: I, Stress Determination for Coulomb Materials, with J.V. Matthews, J. Comput. Phys., 166 (2001), p.63-83.
  • Simulation of Gravity Flow of Granular Materials in Hoppers, with J.V. Matthews, in Discontinuous Galerkin Methods, Theory, Computation and Applications, B. Cockburn, C.W. Shu, G. Karniadakis Eds., Lecture Notes in Computational Science and Engineering, #11 (2000), Springer Verlag, p.125-134.
  • Similarity solution for hopper flows, with J.V. Matthews and M. Shearer, Proceedings of the SIAM/AMS Conference on Nonlinear PDEs, Dynamics and Continuum Physics, J. Bona, K. Saxton, R. Saxton, Eds., AMS Contemporary Mathematics Series, #255 (2000), p.79-95.
  • Numerical Determination of Flow Corrective Inserts for Granular Materials in Conical Hoppers, with D.G. Schaeffer and M. Shearer, Int. J. Nonlinear Mech., 35 (2000), p.869-882.
  • Numerical Simulation of Pattern Formation in Grain Flows, Appl. Math. Comp., 84 (1997), p.145-162.

Error analysis

  • A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws. Part III: Multidimensional Flux -Splitting Monotone Schemes on Non-Cartesian Grids, with B. Cockburn and J.Yang, SIAM J. Numer. Anal., 35 (1998), p.1775-1803.
  • A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws. Part II: Flux -Splitting Monotone Schemes on Irregular Cartesian Grids, with B. Cockburn, Math. Comp., 66 (1997), p.547-572.
  • A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws. Part I: The General Approach, with B. Cockburn, Math. Comp., 65 (1996), p.533-573.
  • An Error Estimate for Finite Element Methods for Scalar Conservation Laws, with B. Cockburn, SIAM J. Numer. Anal., 33 (1996), p.522-554.
  • A New Approach to Numerical Conservation Laws, with B. Cockburn, Comptes Rendus de l'Academie des Sciences, Serie I, 321 (1995), p.481--486.
  • Error Estimates for Euler Forward Scheme Related to Stefan Like Problems, with G. Amiez, Mathematical Modeling and Numerical Analysis, 26 (1992), p.365--383.


  • A simple model for laser drilling, with Jeb Collins, Math. Comput. Simul., 81 (2011), pp.1541--1552.
  • Periodic motion of a mass-spring system, with M. Shearer and K. Kleiner, IMA J. AppliedMathematics, 74 (2009), pp.807--826.
  • Super Time-stepping Acceleration of Explicit Schemes, with V. Alexiades and A. Amiez, Com. Num. Meth. Eng., 12 (1996), p.31-42.