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Selected publications

  • [44] Impedance boundary conditions for general transient hemodynamics, with W. Cousins, submitted.
  • [43] Transcranial Doppler velocity as a measure for cerebral blood flow, with E.G.H.J. Martens, P. Zhao, D.C. Alsop, J.P.H. Reulen, W.H. Mess, F.N. Vosse and V. Novak, submitted.
  • [42] A new physiological boundary condition for hemodynamics, with W. Cousins and D.M. Tartakovsky, SIAM J. Appl. Math., 73 (2013), pp.1203--1223.
  • [41] Granular free surfaces, with Rachael Gordon-Wright, SIAM Rev., 55 (2013), pp.168--184.
  • [40] Numerical study of singularity formation in relativsitic Euler flows, with Yi Sun, accepted in Comm. Comput. Phys.
  • [39] Boundary conditions for hemodynamics: the structured tree revisited, with W. Cousins, J. Comput. Phys., 231 (2012), pp.6086--6096.
  • [38] Analysis of a domain decomposition method for linear transport problems on networks, with J. Collins, submitted to Appl. Num. Math.
  • [37] A simple model for laser drilling, with Jeb Collins, Math. Comput. Simul., 81 (2011), pp.1541--1552 [PDF].
  • [36] 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.
  • [35] Periodic motion of a mass-spring system, with M. Shearer and K. Kleiner, IMA J. AppliedMathematics, 74 (2009), pp.807--826. [PDF].
  • [34] 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. [PDF].
  • [33] Response to perturbations for granular flow in a hopper, with J.F. Wambaugh, J.V. Matthews and R.P. Behringer, Phys. Rev. E, 76 (2007), pp.051303-1--051303-8.
  • [32] Fast numerical methods for Bernoulli free boundary problems, with C.M. Kuster and R. Touzani, SIAM J. Sci. Comput., 29 (2007), pp.622-634. [PDF].
  • [31] 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, [PDF].
  • [30] 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. [PDF].
  • [29] 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.
  • [28] 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, [PDF].
  • [27] Numerical Approximation of p-Systems with Coulomb Frictional Damping, with K. Coffey, NCSU-CRSC Tech Report CRSC-TR04-40, submitted to SIAM J. Sc. Comp., [PDF].
  • [26] Computational Study of Fast Methods for the Eikonal Equation, with C.M. Kuster, SIAM J. Sc. Comp., 27 (2006), p.1803-1816, [PDF].
  • [25] 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, [PDF].
  • [24] 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. [PS], [PDF].
  • [23] Numerical Issues in Plasticity Models for Granular Flows, J. Volcanolgy and Geothermal Res., 139 (2005), p.23-31, [PS], [PDF].
  • [22] 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. [PS], [PDF].
  • [21] Numerical Simulation of Aerated Powder Consolidation, with K.A. Coffey, Int. J. Nonlinear Mech., 38 (2003), p.1185-1194. [PDF] (.8MB).
  • [20] 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. [PS] (.25MB), [PDF].
  • [19] Industrial Mathematics: The 1998 CRSC Workshop, with Zhilin Li, R.C. Smith and H.T. Tran, SIAM 2000, ISBN 0-89871-467-2 (70 pages), [available from SIAM].
  • [18] 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. [ PS] (2MB).
  • [17] 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, [ PDF] (2MB).
  • [16] 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, [ PDF] (.3MB).
  • [15] 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, [ PDF] (.3MB).
  • [14] Computation of Nonclassical Solutions to Hamilton-Jacobi Equations, with N. Ide, SIAM J. Sci. Comput., 21 (1999), p.502-521, [ PDF], (2MB).
  • [13] 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, [ PS], [ PDF] (0.5 MB).
  • [12] 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, [ PS], [ PDF] (0.4 MB).
  • [11] 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, [PS], [ PDF] (0.4 MB).
  • [10] Numerical Simulation of Pattern Formation in Grain Flows, Appl. Math. Comp., 84 (1997), p.145-162. [ PS] (1.1 MB), [ PDF], (0.6 MB).
  • [9] Super Time-stepping Acceleration of Explicit Schemes, with V. Alexiades and A. Amiez, Com. Num. Meth. Eng., 12 (1996), p.31-42. [ PS], [ PDF], (0.3 MB).
  • [8] An Error Estimate for Finite Element Methods for Scalar Conservation Laws, with B. Cockburn, SIAM J. Numer. Anal., 33 (1996), p.522-554. [ PS], [ PDF], (0.4 MB).
  • [7] A New Approach to Numerical Conservation Laws, with B. Cockburn, Comptes Rendus de l'Academie des Sciences, Serie I, 321 (1995), p.481--486.
  • [6] Numerical Optimization and Quasiconvexity, European J. Appl. Math., 6 (1995), p.69--82.
  • [5] Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions, SIAM J. Numer. Anal., 31 (1994), p.111--127.
  • [4] On an Elliptic-Parabolic Problem Related to Phase Transitions in Shape Memory Alloys, Numer. Funct. Anal. Opt., 14 (1993), p.355--370.
  • [3] 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.
  • [2] Error Estimates for Euler Forward Scheme Related to Stefan Like Problems, with G. Amiez, Mathematical Modeling and Numerical Analysis, 26 (1992), p.365--383.
  • [1] On a Numerical Approach to Stefan Like Problems, with G. Amiez, Numer.Math, 59 (1991), p.71--89.