Pierre Gremaud Gamboa, F., Gremaud, P., Klein, T., & Lagnoux, A. (2022). Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics. BERNOULLI, 28(4), 2345–2374. https://doi.org/10.3150/21-BEJ1421 Gilmore, S., Hart, J., Geddes, J., Olsen, C. H., Mehlsen, J., Gremaud, P., & Olufsen, M. S. (2021). Classification of orthostatic intolerance through data analytics. MEDICAL & BIOLOGICAL ENGINEERING & COMPUTING, 59(3), 621–632. https://doi.org/10.1007/s11517-021-02314-0 Merritt, M., Alexanderian, A., & Gremaud, P. A. (2021). MULTISCALE GLOBAL SENSITIVITY ANALYSIS FOR STOCHASTIC CHEMICAL SYSTEMS. MULTISCALE MODELING & SIMULATION, 19(1), 440–459. https://doi.org/10.1137/20M1323989 Alexanderian, A., Gremaud, P. A., & Smith, R. C. (2020). Variance-based sensitivity analysis for time-dependent processes. RELIABILITY ENGINEERING & SYSTEM SAFETY, 196. https://doi.org/10.1016/j.ress.2019.106722 Williams, N. D., Brady, R., Gilmore, S., Gremaud, P., Tran, H. T., Ottesen, J. T., … Olufsen, M. S. (2019). Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models. Journal of Mathematical Biology, 79(3), 987–1014. https://doi.org/10.1007/s00285-019-01386-9 Schaeffer, D. G., Barker, T., Tsuji, D., Gremaud, P., Shearer, M., & Gray, J. M. N. T. (2019). Constitutive relations for compressible granular flow in the inertial regime. JOURNAL OF FLUID MECHANICS, 874, 926–951. https://doi.org/10.1017/jfm.2019.476 Hart, J. L., Gremaud, P. A., & David, T. (2019). Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling. BULLETIN OF MATHEMATICAL BIOLOGY, 81(6), 1805–1828. https://doi.org/10.1007/s11538-019-00578-0 Hart, J., & Gremaud, P. (2019). ROBUSTNESS OF THE SOBOL' INDICES TO DISTRIBUTIONAL UNCERTAINTY. INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 9(5), 453–469. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019030553 Hart, J. L., & Gremaud, P. A. (2019). Robustness of the Sobol' Indices to Marginal Distribution Uncertainty. SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 7(4), 1224–1244. https://doi.org/10.1137/18M123387X Hart, J. L., & Gremaud, P. A. (2018). AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES. INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION, 8(6), 483–493. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2018026498 Maltba, T., Gremaud, P. A., & Tartakoysky, D. M. (2018). Nonlocal PDF methods for Langevin equations with colored noise. JOURNAL OF COMPUTATIONAL PHYSICS, 367, 87–101. https://doi.org/10.1016/j.jcp.2018.04.023 Hart, J. L., Alexanderian, A., & Gremaud, P. A. (2017). EFFICIENT COMPUTATION OF SOBOL' INDICES FOR STOCHASTIC MODELS. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 39(4), A1514–A1530. https://doi.org/10.1137/16m106193x Collins, J. B., & Gremaud, P. A. (2016). Analysis of a domain decomposition method for linear transport problems on networks. APPLIED NUMERICAL MATHEMATICS, 109, 61–72. https://doi.org/10.1016/j.apnum.2016.06.004 Guan, D., Liang, F., & Gremaud, P. A. (2016). Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model. JOURNAL OF BIOMECHANICS, 49(9), 1583–1592. https://doi.org/10.1016/j.jbiomech.2016.03.037 Hart, J., Novak, V., Saunders, C., & Gremaud, P. A. (2016). Transcranial Doppler-Based Surrogates for Cerebral Blood Flow: A Statistical Study. PLOS ONE, 11(11). https://doi.org/10.1371/journal.pone.0165536 Cousins, W., & Gremaud, P. A. (2014). Impedance boundary conditions for general transient hemodynamics. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, 30(11), 1294–1313. https://doi.org/10.1002/cnm.2658 Gremaud, P. A., & Sun, Y. (2014). Numerical Study of Singularity Formation in Relativistic Euler Flows. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 16(2), 348–364. https://doi.org/10.4208/cicp.221212.300114a Cousins, W., Gremaud, P. A., & Tartakovsky, D. M. (2013). A NEW PHYSIOLOGICAL BOUNDARY CONDITION FOR HEMODYNAMICS. SIAM JOURNAL ON APPLIED MATHEMATICS, 73(3), 1203–1223. https://doi.org/10.1137/120895470 Gordon-Wright, R., & Gremaud, P. A. (2013). Granular Free Surfaces. SIAM REVIEW, 55(1), 168–184. https://doi.org/10.1137/090747944 Cousins, W., & Gremaud, P. A. (2012). Boundary conditions for hemodynamics: The structured tree revisited. JOURNAL OF COMPUTATIONAL PHYSICS, 231(18), 6086–6096. https://doi.org/10.1016/j.jcp.2012.04.038 Collins, J., & Gremaud, P. (2011). A simple model for laser drilling. MATHEMATICS AND COMPUTERS IN SIMULATION, 81(8), 1541–1552. https://doi.org/10.1016/j.matcom.2010.07.010 Shearer, M., Gremaud, P., & Kleiner, K. (2009). Periodic motion of a mass-spring system. IMA JOURNAL OF APPLIED MATHEMATICS, 74(6), 807–826. https://doi.org/10.1093/imamat/hxp032 Devault, K., Gremaud, P. A., Novak, V., Olufsen, M. S., Vernieres, G., & Zhao, P. (2008). BLOOD FLOW IN THE CIRCLE OF WILLIS: MODELING AND CALIBRATION. MULTISCALE MODELING & SIMULATION, 7(2), 888–909. https://doi.org/10.1137/07070231X Gremaud, P. A., Kuster, C. M., & Li, Z. (2007). A study of numerical methods for the level set approach. APPLIED NUMERICAL MATHEMATICS, Vol. 57, pp. 837–846. https://doi.org/10.1016/j.apnum.2006.07.022 Kuster, C. M., Gremaud, P. A., & Touzani, R. (2007). Fast numerical methods for Bernoulli free boundary problems. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 29(2), 622–634. https://doi.org/10.1137/06065444X Devault, K. J., Gremaud, P. A., & Jenssen, H. K. (2007). Numerical investigation of cavitation in multidimensional compressible flows. SIAM JOURNAL ON APPLIED MATHEMATICS, 67(6), 1675–1692. https://doi.org/10.1137/060652713 Wambaugh, J. F., Behringer, R. P., Matthews, J. V., & Gremaud, P. A. (2007). Response to perturbations for granular flow in a hopper. PHYSICAL REVIEW E, 76(5). https://doi.org/10.1103/physreve.76.051303 Gremaud, P. A., & Kuster, C. M. (2006). Computational study of fast methods for the eikonal equation. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 27(6), 1803–1816. https://doi.org/10.1137/040605655 Gremaud, P. A., Matthews, J. V., & Schaeffer, D. G. (2006). On the computation of steady hopper flows III: Model comparisons. JOURNAL OF COMPUTATIONAL PHYSICS, 219(1), 443–454. https://doi.org/10.1016/j.jcp.2006.03.032 Gremaud, P. A. (2005). Numerical issues in plasticity models for granular materials. JOURNAL OF VOLCANOLOGY AND GEOTHERMAL RESEARCH, 139(1-2), 23–31. https://doi.org/10.1016/j.jvolgeores.2004.06.018 Gremaud, P. A., Matthews, J. V., & M O'Malley. (2004). On the computation of steady Hopper flows II: von Mises materials in various geometries. JOURNAL OF COMPUTATIONAL PHYSICS, 200(2), 639–653. https://doi.org/10.1016/j.jcp.2004.04.021 Ahmed, S. A., Buckingham, R., Gremaud, P. A., Hauck, C. D., Kuster, C. M., Prodanovic, M., … Silantyev, V. (2004). Volume determination for bulk materials in bunkers. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 61(13), 2239–2249. https://doi.org/10.1002/nme.1144 Coffey, K. A., & Gremaud, P. A. (2003). Numerical simulation of aerated powder consolidation. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 38(8), 1185–1194. https://doi.org/10.1016/S0020-7462(02)00063-X Gremaud, P. A., Matthews, J. V., & Schaeffer, D. G. (2003). Secondary circulation in granular flow through nonaxisymmetric hoppers. SIAM JOURNAL ON APPLIED MATHEMATICS, 64(2), 583–600. https://doi.org/10.1137/S0036139903415124 Gremaud, P. A., Kelley, C. T., Royal, T. A., & Coffey, K. A. (2001). On a powder consolidation problem. SIAM Journal on Applied Mathematics, 62(1), 1–20. https://doi.org/10.1137/s0036139900368479 Gremaud, P. A., & Matthews, J. V. (2001). On the computation of steady hopper flows I. Stress determination for Coulomb materials. JOURNAL OF COMPUTATIONAL PHYSICS, 166(1), 63–83. https://doi.org/10.1006/jcph.2000.6641 Gremaud, P. A., Schaeffer, D. G., & Shearer, M. (2000). Numerical determination of flow corrective inserts for granular materials in conical hoppers. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 35(5), 869–882. https://doi.org/10.1016/S0020-7462(99)00064-5 Gremaud, P. A., & Ide, N. R. (1999). Computation of nonclassical solutions to Hamilton-Jacobi problems. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 21(2), 502–521. https://doi.org/10.1137/S1064827597327668 Cockburn, B., Gremaud, P. A., & Yang, J. X. R. (1998). A priori error estimates for numerical methods for scalar conservation laws - Part III: Multidimensional flux-splitting monotone schemes on non-Cartesian grids. SIAM JOURNAL ON NUMERICAL ANALYSIS, 35(5), 1775–1803. https://doi.org/10.1137/S0036142997316165 Gremaud, P. A. (1997). Numerical simulation of pattern formation in grain flows. APPLIED MATHEMATICS AND COMPUTATION, 84(2-3), 145–162. https://doi.org/10.1016/S0096-3003(96)00084-7 Cockburn, B., & Gremaud, P. A. (1997). a priori error estimates for numerical methods for scalar conservation laws .2. Flux-splitting monotone schemes on irregular Cartesian grids. MATHEMATICS OF COMPUTATION, 66(218), 547–572. https://doi.org/10.1090/S0025-5718-97-00838-7 Cockburn, B., & Gremaud, P. A. (1996). Error estimates for finite element methods for scalar conservation laws. SIAM JOURNAL ON NUMERICAL ANALYSIS, 33(2), 522–554. https://doi.org/10.1137/0733028 GREMAUD, P. A. (1994). NUMERICAL-ANALYSIS OF A NONCONVEX VARIATIONAL PROBLEM RELATED TO SOLID-SOLID PHASE-TRANSITIONS. SIAM JOURNAL ON NUMERICAL ANALYSIS, 31(1), 111–127. https://doi.org/10.1137/0731006 AMIEZ, G., & GREMAUD, P. A. (1992). ERROR-ESTIMATES FOR EULER FORWARD SCHEME RELATED TO 2-PHASE STEFAN-PROBLEMS. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 26(2), 365–383. https://doi.org/10.1051/m2an/1992260203651