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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 Dopplerbased surrogates for cerebral blood
flow: a statistical study, with J. Hart, V. Novak, C. Saunders, submitted.
 Comparison of the Windkessel model and structuredtree model
applied to prescribe outflow boundary conditions for a onedimensional
arterial tree model, with D. Guan and F. Liang, J.
Biomechanics, 49 (2016), pp.15831592.
 Impedance boundary conditions for general transient
hemodynamics, with W. Cousins, Int. J. Numer. Biomed.
Eng., 30 (2014), pp.12941313.
 A new physiological boundary condition for hemodynamics,
with W. Cousins and D.M. Tartakovsky, SIAM J.
Appl. Math., 73 (2013), pp.12031223.
 Boundary conditions for hemodynamics: the structured
tree revisited, with W. Cousins, J. Comput. Phys., 231
(2012), pp.60866096.
 Modeling cerebral blood flow and regulation, with
M.C. Aoi, H.T. Tran, V. Novak and M. Olufsen, Eng. Med. Biol.
Soc., 2009, pp.24102413.
 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.888909.
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.6172.
 Numerical study of singularity formation in relativistic
Euler flows, with Yi Sun, Comm. Comput. Phys., 16 (2014),
pp.348364.
 Numerical Investigation of Cavitation in Multidimensional Compressible Flows,
with K.J. DeVault and H.K. Jenssen,
SIAM J. Appl. Math., 67 (2007), pp.16751692.
 On a Penalty Method for the NavierStokes Problem in Regions with
Moving Boundaries, with G. Amiez, Mat. Aplic. Com., 12 (1993),
p.113123.
HamiltonJacobi, 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.622634.
 A Study of Numerical Methods for the Level Set Approach,
with C.M. Kuster and
Zhilin Li, Applied Numerical Mathematics, 57 (2007),
pp.837846.
 Computational Study of Fast Methods for the Eikonal
Equation, with C.M. Kuster,
SIAM J. Sc. Comp., 27 (2006), p.18031816.
 Computation of Nonclassical Solutions to HamiltonJacobi
Equations, with N. Ide, SIAM J. Sci. Comput., 21 (1999),
p.502521.
 Numerical Analysis of a Nonconvex Variational Problem Related to
SolidSolid Phase Transitions, SIAM J. Numer. Anal., 31 (1994), p.111127.
 On an EllipticParabolic Problem Related to Phase Transitions in
Shape Memory Alloys, Numer. Funct. Anal. Opt., 14 (1993), p.355370.
 On a Numerical Approach to Stefan Like Problems, with G. Amiez,
Numer.Math, 59 (1991), p.7189.
Granular materials
 Granular free surfaces, with Rachael
GordonWright, SIAM Rev., 55 (2013),
pp.168184.
 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.305312.
 On the Computation of Steady Hopper Flows III: Model
Comparisons, with J.V. Matthews and D.G. Schaeffer,
J. Comp. Phys., 219 (2006), p.443454.
 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.639653.
 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.22392249.
 Numerical Issues in Plasticity Models for Granular Flows,
J. Volcanolgy and Geothermal Res., 139 (2005), p.2331,
 Secondary Circulation in Granular Flows through Axisymmetric Hoppers,
with J.V. Matthews and D.G. Schaeffer,
SIAM J. Appl. Math., 64 (2003), p.583600.
 Numerical Simulation of Aerated Powder Consolidation, with K.A. Coffey,
Int. J. Nonlinear Mech., 38 (2003), p.11851194.
 On a Powder Consolidation Problem, with C.T. Kelley, T.A. Royal and K.A. Coffey,
SIAM J. Appl. Math., 62 (2001), pp.120.
 On the Computation of Steady Hopper Flows: I, Stress
Determination for Coulomb Materials, with J.V. Matthews,
J. Comput. Phys., 166
(2001), p.6383.
 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.125134.
 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.7995.
 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.869882.
 Numerical Simulation of Pattern Formation in Grain Flows,
Appl. Math. Comp., 84 (1997), p.145162.
Error analysis
 A Priori Error Estimates for Numerical Methods for Scalar
Conservation Laws. Part III: Multidimensional Flux Splitting Monotone
Schemes on NonCartesian Grids, with B. Cockburn and J.Yang,
SIAM J. Numer. Anal., 35 (1998), p.17751803.
 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.547572.
 A Priori Error Estimates for Numerical Methods for Scalar
Conservation Laws. Part I: The General Approach, with B. Cockburn,
Math. Comp., 65 (1996), p.533573.
 An Error Estimate for Finite Element Methods for Scalar
Conservation Laws, with B. Cockburn, SIAM J. Numer. Anal., 33 (1996),
p.522554.
 A New Approach to Numerical Conservation Laws,
with B. Cockburn, Comptes Rendus de l'Academie des Sciences,
Serie I, 321 (1995), p.481486.
 Error Estimates for Euler Forward Scheme Related to Stefan Like Problems,
with G. Amiez, Mathematical Modeling and Numerical Analysis, 26 (1992),
p.365383.
Miscellaneous
 A simple model for laser drilling, with Jeb
Collins, Math. Comput. Simul., 81 (2011), pp.15411552.
 Periodic motion of a massspring system, with M. Shearer
and K. Kleiner, IMA J. AppliedMathematics, 74 (2009), pp.807826.
 Super Timestepping Acceleration of Explicit Schemes,
with V. Alexiades and A. Amiez, Com. Num. Meth. Eng., 12 (1996),
p.3142.
