Pierre Alain Gremaud

Works (45)

Updated: March 8th, 2025 05:01

2024 article

VARIANCE-BASED SENSITIVITY OF BAYESIAN INVERSE PROBLEMS TO THE PRIOR DISTRIBUTION

Darges, J., Alexanderian, A., & Gremaud, P. (2024, August 14). International Journal for Uncertainty Quantification, Vol. 15, pp. 65–90.

By: J. Darges, A. Alexanderian*  & P. Gremaud*

author keywords: prior hyperparameters; global sensitivity analysis; Sobol' indices; Bayesian inverse problems; importance sampling; surrogate modeling
topics (OpenAlex): Gaussian Processes and Bayesian Inference; Bayesian Methods and Mixture Models
Sources: Web Of Science, NC State University Libraries
Added: March 3, 2025

2022 article

Global sensitivity analysis: A novel generation of mighty estimators based on rank statistics

Gamboa, F., Gremaud, P., Klein, T., & Lagnoux, A. (2022, August 29). Bernoulli.

By: F. Gamboa *, P. Gremaud n, T. Klein * & A. Lagnoux *

author keywords: Global sensitivity analysis; Cram?r-von-Mises distance; Pick-Freeze method; Chatterjee?s coefficient of correlation; Sobol? indices estimation
topics (OpenAlex): Probabilistic and Robust Engineering Design; Fatigue and fracture mechanics; Statistical Distribution Estimation and Applications
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Source: Web Of Science
Added: September 6, 2022

2021 article

Classification of orthostatic intolerance through data analytics

Gilmore, S., Hart, J., Geddes, J., Olsen, C. H., Mehlsen, J., Gremaud, P., & Olufsen, M. S. (2021, February 13). Medical & Biological Engineering & Computing.

By: S. Gilmore n, J. Hart *, J. Geddes n, C. Olsen*, J. Mehlsen *, P. Gremaud n, M. Olufsen n

author keywords: Orthostatic intolerance; Syncope; Classification; Clustering; Machine learning
MeSH headings : Autonomic Nervous System; Blood Pressure; Data Science; Heart Rate; Humans; Orthostatic Intolerance / diagnosis; Syncope / diagnosis; Tilt-Table Test
topics (OpenAlex): Cardiovascular Syncope and Autonomic Disorders; Heart Rate Variability and Autonomic Control; Respiratory and Cough-Related Research
TL;DR: This study uses machine learning to categorize patients with orthostatic intolerance and shows that machine learning can provide accurate classification of disease groups for 98% of patients and two subgroups within the control patients differentiated by their BP response. (via Semantic Scholar)
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Source: Web Of Science
Added: March 8, 2021

2021 article

Multiscale Global Sensitivity Analysis for Stochastic Chemical Systems

Merritt, M., Alexanderian, A., & Gremaud, P. A. (2021, January 1). Multiscale Modeling and Simulation.

By: M. Merritt*, A. Alexanderian*  & P. Gremaud*

author keywords: chemical reaction networks; stochastic processes; global sensitivity analysis; multiscale modeling; thermodynamic limit
topics (OpenAlex): Gene Regulatory Network Analysis; Probabilistic and Robust Engineering Design; stochastic dynamics and bifurcation; thermodynamics and calorimetric analyses
TL;DR: A full justification of the above approach in the case of variance based methods provided the surrogate model results from the original one through the thermodynamic limit is provided. (via Semantic Scholar)
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Source: Web Of Science
Added: May 3, 2021

2019 journal article

Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models

Journal of Mathematical Biology, 79(3), 987–1014.

By: N. Williams*, R. Brady *, S. Gilmore  n, P. Gremaud n, H. Tran n , J. Ottesen*, J. Mehlsen *, M. Olufsen n

author keywords: Cardiovascular dynamics modeling; Head-up tilt; Pulsatile versus non-pulsatile modeling; Parameter estimation; Orthostatic intolerance
MeSH headings : Adult; Blood Pressure; Cardiac Output / physiology; Heart Rate; Hemodynamics; Humans; Male; Models, Cardiovascular; Pulsatile Flow; Supine Position; Tilt-Table Test; Vascular Resistance / physiology
topics (OpenAlex): Cardiovascular Health and Disease Prevention; Heart Rate Variability and Autonomic Control; Cardiovascular Syncope and Autonomic Disorders; Non-Invasive Vital Sign Monitoring
TL;DR: It is shown that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system’s state. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries, Crossref
Added: August 19, 2019

2019 article

Constitutive relations for compressible granular flow in the inertial regime

Schaeffer, D. G., Barker, T., Tsuji, D., Gremaud, P., Shearer, M., & Gray, J. M. N. T. (2019, July 15). Journal of Fluid Mechanics, Vol. 874, pp. 926–951.

By: D. Schaeffer*, T. Barker *, D. Tsuji*, P. Gremaud n, M. Shearer n  & J. Gray *

author keywords: granular media; rheology
topics (OpenAlex): Granular flow and fluidized beds; Landslides and related hazards; Soil and Unsaturated Flow
Sources: Web Of Science, NC State University Libraries
Added: August 12, 2019

2019 article

Global Sensitivity Analysis of High-Dimensional Neuroscience Models: An Example of Neurovascular Coupling

Hart, J. L., Gremaud, P. A., & David, T. (2019, February 28). Bulletin of Mathematical Biology.

By: J. Hart n, P. Gremaud n & T. David *

author keywords: Neurovascular coupling; Global sensitivity analysis; Model parameters
MeSH headings : Actomyosin / physiology; Algorithms; Animals; Blood Flow Velocity / physiology; Computer Simulation; Extracellular Space / physiology; Humans; Mathematical Concepts; Models, Neurological; Neurovascular Coupling / physiology; Potassium / physiology; Signal Transduction / physiology; Vascular Resistance / physiology
topics (OpenAlex): Gene Regulatory Network Analysis; Protein Structure and Dynamics; Probabilistic and Robust Engineering Design
TL;DR: Global sensitivity analysis provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation. (via Semantic Scholar)
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Source: Web Of Science
Added: June 17, 2019

2019 article

ROBUSTNESS OF THE SOBOL' INDICES TO DISTRIBUTIONAL UNCERTAINTY

Hart, J., & Gremaud, P. A. (2019, January 1). International Journal for Uncertainty Quantification.

By: J. Hart n & P. Gremaud n

author keywords: global sensitivity analysis; Sobol' indices; uncertain distributions; deep uncertainty
topics (OpenAlex): Probabilistic and Robust Engineering Design; Fatigue and fracture mechanics; Structural Response to Dynamic Loads
TL;DR: The robustness of the Sobol' indices, a commonly used tool in GSA, to changes in the distribution of the uncertain variables is analyzed, which requires minimal user specification and no additional evaluations of the model. (via Semantic Scholar)
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Added: January 6, 2020

2019 article

Robustness of the Sobol' Indices to Marginal Distribution Uncertainty

Hart, J. L., & Gremaud, P. A. (2019, January 1). SIAM/ASA Journal on Uncertainty Quantification.

By: J. Hart* & P. Gremaud*

author keywords: global sensitivity analysis; Sobol' indices; robustness; epistemic uncertainty
topics (OpenAlex): Probabilistic and Robust Engineering Design; Structural Response to Dynamic Loads; Fatigue and fracture mechanics; Nuclear reactor physics and engineering
TL;DR: A novel method which uses "optimal perturbations" of the marginal probability density functions to analyze the robustness of the Sobol' indices is presented. (via Semantic Scholar)
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Added: August 10, 2020

2019 article

Variance-based sensitivity analysis for time-dependent processes

Alexanderian, A., Gremaud, P. A., & Smith, R. C. (2019, November 4). Reliability Engineering & System Safety, Vol. 196.

By: A. Alexanderian n , P. Gremaud n & R. Smith n 

author keywords: Global sensitivity analysis; Sobol' Indices; Karhunen-Loeve expansion; Time-dependent processes; Surrogate models; Polynomial chaos; Uncertainty quantification
topics (OpenAlex): Probabilistic and Robust Engineering Design; Model Reduction and Neural Networks; Control Systems and Identification
TL;DR: A variance-based method is developed that leverages the correlation structure of the problems under study and employs surrogate models to accelerate the computations and analyzes errors resulting from fixing unimportant uncertain parameters to their nominal values through a priori estimates. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: March 16, 2020

2018 article

AN APPROXIMATION THEORETIC PERSPECTIVE OF SOBOL' INDICES WITH DEPENDENT VARIABLES

Hart, J. L., & Gremaud, P. A. (2018, January 1). International Journal for Uncertainty Quantification.

By: J. Hart* & P. Gremaud n

author keywords: global sensitivity analysis; Sobol' indices; dependent variables
topics (OpenAlex): Probabilistic and Robust Engineering Design; Fatigue and fracture mechanics; Nuclear reactor physics and engineering
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Source: Web Of Science
Added: December 10, 2018

2018 article

Nonlocal PDF methods for Langevin equations with colored noise

Maltba, T., Gremaud, P. A., & Tartakovsky, D. M. (2018, April 13). Journal of Computational Physics.

By: T. Maltba *, P. Gremaud n & D. Tartakovsky *

author keywords: PDF method; Nonlocal; Langevin equation; Colored noise; Stochastic; Random; Uncertainty quantification
topics (OpenAlex): Probabilistic and Robust Engineering Design; Model Reduction and Neural Networks; Fractional Differential Equations Solutions
TL;DR: A new semi-local formulation based on a modified large-eddy diffusivity (LED) approach is proposed; the formulation retains most of the accuracy of a fully nonlocal approach while presenting the same order of algorithmic complexity as the standard LED approach. (via Semantic Scholar)
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Added: August 6, 2018

2017 article

Efficient Computation of Sobol' Indices for Stochastic Models

Hart, J. L., Alexanderian, A., & Gremaud, P. A. (2017, January 1). SIAM Journal on Scientific Computing.

By: J. Hart*, A. Alexanderian*  & P. Gremaud*

author keywords: global sensitivity; Sobol' indices; stochastic models; surrogate models; MARS; high dimensions
topics (OpenAlex): Probabilistic and Robust Engineering Design; Advanced Multi-Objective Optimization Algorithms; Structural Response to Dynamic Loads; Model Reduction and Neural Networks
TL;DR: This work presents a new global sensitivity analysis approach for stochastic models, i.e., models with both uncertain parameters and intrinsic Stochasticity, which relies on an analysis of variance through a generalization of Sobol' indices and on the use of surrogate models. (via Semantic Scholar)
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Added: August 6, 2018

2016 article

Analysis of a domain decomposition method for linear transport problems on networks

Collins, J. B., & Gremaud, P. A. (2016, June 26). Applied Numerical Mathematics.

By: J. Collins* & P. Gremaud n

author keywords: Transport; Network; Domain decomposition
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Probabilistic and Robust Engineering Design; Numerical methods in engineering
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Source: Web Of Science
Added: August 6, 2018

2016 article

Comparison of the Windkessel model and structured-tree model applied to prescribe outflow boundary conditions for a one-dimensional arterial tree model

Guan, D., Liang, F., & Gremaud, P. A. (2016, March 30). Journal of Biomechanics.

By: D. Guan *, F. Liang * & P. Gremaud n

author keywords: One-dimensional model; Arterial tree; Outflow boundary conditions; Windkessel model; Structured-tree model; Pressure wave
MeSH headings : Arteries / physiology; Blood Pressure; Hemodynamics; Humans; Models, Cardiovascular
topics (OpenAlex): Cardiovascular Health and Disease Prevention; Coronary Interventions and Diagnostics; Cardiovascular Function and Risk Factors
TL;DR: It is suggested that the method adopted for modeling the outflow boundary conditions has considerable influence on the performance of a 1D arterial tree model, with the extent of influence varying with the properties of the arterial system. (via Semantic Scholar)
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Added: August 6, 2018

2016 article

Transcranial Doppler-Based Surrogates for Cerebral Blood Flow: A Statistical Study

Hart, J., Novak, V., Saunders, C., & Gremaud, P. A. (2016, November 23). PLoS ONE.

By: J. Hart n, V. Novak *, C. Saunders* & P. Gremaud n

MeSH headings : Aged; Algorithms; Blood Flow Velocity / physiology; Cerebral Arteries / diagnostic imaging; Cerebrovascular Circulation / physiology; Female; Humans; Magnetic Resonance Angiography; Male; Middle Aged; Models, Statistical; Ultrasonography, Doppler, Transcranial
topics (OpenAlex): Advanced MRI Techniques and Applications; Cerebrovascular and Carotid Artery Diseases; Cardiovascular Health and Disease Prevention
TL;DR: A cerebral blood flow estimator is constructed based on transcranial Doppler blood flow velocity and ten other easily available patient characteristics and clinical parameters to test the hypothesis that perfusion in a given cerebral territory can be inferred from Blood Flow Velocity measurements in the corresponding stem artery. (via Semantic Scholar)
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Added: August 6, 2018

2014 article

Impedance boundary conditions for general transient hemodynamics

Cousins, W., & Gremaud, P. A. (2014, June 23). International Journal for Numerical Methods in Biomedical Engineering.

By: W. Cousins * & P. Gremaud n

author keywords: hemodynamics; boundary conditions; autoregulation; impedance; vascular trees
MeSH headings : Algorithms; Aorta / physiology; Blood Vessels / physiology; Cerebral Arteries / physiology; Circle of Willis / physiology; Hemodynamics; Humans; Models, Cardiovascular
topics (OpenAlex): Cardiovascular Health and Disease Prevention; Cardiovascular Function and Risk Factors; Traumatic Brain Injury and Neurovascular Disturbances
TL;DR: A novel way to incorporate autoregulation mechanisms in structured arterial trees at minimal computational cost is described and illustrated and validated on several examples through comparison with clinical data. (via Semantic Scholar)
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Added: August 6, 2018

2014 article

Numerical Study of Singularity Formation in Relativistic Euler Flows

Gremaud, P. A., & Sun, Y. (2014, August 1). Communications in Computational Physics.

By: P. Gremaud n & Y. Sun *

author keywords: Relativistic Euler equations; singularity formation; Glimm scheme; central-upwind scheme; hybrid method
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Gas Dynamics and Kinetic Theory; Fluid Dynamics and Turbulent Flows
Source: Web Of Science
Added: August 6, 2018

2013 article

A New Physiological Boundary Condition for Hemodynamics

Cousins, W., Gremaud, P. A., & Tartakovsky, D. M. (2013, January 1). SIAM Journal on Applied Mathematics.

By: W. Cousins*, P. Gremaud* & D. Tartakovsky

author keywords: hemodynamics; network; transport; modeling; boundary conditions; numerics
topics (OpenAlex): Advanced MRI Techniques and Applications; Cardiovascular Health and Disease Prevention; Cardiovascular Function and Risk Factors
TL;DR: This study proposes a new physiologically-based outflow boundary condition for hemodynamics under general transient regimes that has better stability properties and provides a partial justification for using some of these existing conditions beyond the periodic problems for which they were designed. (via Semantic Scholar)
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Added: August 6, 2018

2013 article

Granular Free Surfaces

Gordon-Wright, R., & Gremaud, P. A. (2013, January 1). SIAM Review.

By: R. Gordon-Wright* & P. Gremaud*

author keywords: free surfaces; friction; mechanics; granular material; differential inclusions; partial differential equations
topics (OpenAlex): Granular flow and fluidized beds; Experimental and Theoretical Physics Studies; Sports Dynamics and Biomechanics
TL;DR: The notion of angle of repose for granular materials is explored and the free surface problems for centrifuged granular piles are solved. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2012 article

Boundary conditions for hemodynamics: The structured tree revisited

Cousins, W., & Gremaud, P. A. (2012, May 26). Journal of Computational Physics.

By: W. Cousins n & P. Gremaud n

author keywords: Hemodynamics; Network; Transport; Modeling; Boundary conditions; Numerics
topics (OpenAlex): Cardiovascular Health and Disease Prevention; Cardiovascular Function and Risk Factors; Fluid Dynamics and Turbulent Flows
TL;DR: This work proposes an alternative derivation of the structured tree boundary condition that is considerably simpler than the original one and yields similar, but not identical, results. (via Semantic Scholar)
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Added: August 6, 2018

2010 article

A simple model for laser drilling

Collins, J., & Gremaud, P. (2010, August 4). Mathematics and Computers in Simulation.

By: J. Collins n & P. Gremaud n

author keywords: Laser drilling; Phase change; Free boundary; Numerical methods
topics (OpenAlex): Laser Material Processing Techniques; Advanced Surface Polishing Techniques; Welding Techniques and Residual Stresses
TL;DR: A simple mathematical model of laser drilling is proposed, assuming axi-symmetry of the process around the axis of the laser beam, and a one-dimensional formulation is obtained after cross-sectional averaging. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2009 article

Periodic motion of a mass-spring system

Shearer, M., Gremaud, P., & Kleiner, K. (2009, October 27). IMA Journal of Applied Mathematics, Vol. 74, pp. 807–826.

By: M. Shearer n , P. Gremaud n & K. Kleiner n

author keywords: mass-spring system; Hamiltonian system; periodic solutions
topics (OpenAlex): Quantum chaos and dynamical systems; Experimental and Theoretical Physics Studies; Control and Dynamics of Mobile Robots
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2008 article

Blood Flow in the Circle of Willis: Modeling and Calibration

DeVault, K., Gremaud, P. A., Novak, V., Olufsen, M. S., Vernières, G., & Zhao, P. (2008, January 1). Multiscale Modeling and Simulation.

By: K. DeVault n, P. Gremaud*, V. Novak*, M. Olufsen*, G. Vernières & P. Zhao

author keywords: blood flow; viscoelastic arteries; fluid-structure interaction; Kalman filtering
topics (OpenAlex): Cardiovascular Health and Disease Prevention; Advanced Neuroimaging Techniques and Applications; MRI in cancer diagnosis
TL;DR: A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data and demonstrates the viability of the proposed approach on the circle of Willis, a vital subnetwork of the cerebral vasculature. (via Semantic Scholar)
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Added: August 6, 2018

2007 article

Fast Numerical Methods for Bernoulli Free Boundary Problems

Kuster, C. M., Gremaud, P. A., & Touzani, R. (2007, January 1). SIAM Journal on Scientific Computing.

By: C. Kuster*, P. Gremaud* & R. Touzani *

author keywords: Bernoulli; free boundary; level set; boundary elements
topics (OpenAlex): Numerical methods in engineering; Advanced Numerical Methods in Computational Mathematics; Electromagnetic Simulation and Numerical Methods
TL;DR: The numerical solution of the free boundary Bernoulli problem is addressed and an iterative method based on a level-set formulation and boundary element method is proposed. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2007 article

Numerical Investigation of Cavitation in Multidimensional Compressible Flows

DeVault, K. J., Gremaud, P. A., & Jenssen, H. K. (2007, January 1). SIAM Journal on Applied Mathematics.

By: K. DeVault n, P. Gremaud n & H. Jenssen

author keywords: Navier-Stokes; Euler; compressible fl ow; cavitation; pseudospectral
topics (OpenAlex): Navier-Stokes equation solutions; Computational Fluid Dynamics and Aerodynamics; Fluid Dynamics and Turbulent Flows
TL;DR: The numerical results indicate that there are weak solutions to the Navier–Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. (via Semantic Scholar)
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Source: Web Of Science
Added: August 6, 2018

2007 article

Response to perturbations for granular flow in a hopper

Wambaugh, J. F., Behringer, R. P., Matthews, J. V., & Gremaud, P. A. (2007, November 14). Physical Review E.

By: J. Wambaugh *, R. Behringer *, J. Matthews * & P. Gremaud n

topics (OpenAlex): Granular flow and fluidized beds; Landslides and related hazards; Sports Dynamics and Biomechanics
TL;DR: Experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting is found and the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. (via Semantic Scholar)
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10. Reduced Inequalities (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2006 article

A study of numerical methods for the level set approach

Gremaud, P. A., Kuster, C. M., & Li, Z. (2006, August 15). Applied Numerical Mathematics, Vol. 57, pp. 837–846.

By: P. Gremaud n, C. Kuster n & Z. Li n 

topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Advanced Numerical Analysis Techniques; Computational Geometry and Mesh Generation
TL;DR: Two types of reinitialization methods are studied: a high order ''PDE'' approach and a second order Fast Marching method, with emphasis on the tube/narrow band implementation and accuracy considerations. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2006 article

Computational Study of Fast Methods for the Eikonal Equation

Gremaud, P. A., & Kuster, C. M. (2006, January 1). SIAM Journal on Scientific Computing.

By: P. Gremaud n & C. Kuster n

author keywords: Hamilton-Jacobi; eikonal; viscosity solution; fast marching; fast sweeping
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Numerical methods for differential equations; Computational Fluid Dynamics and Aerodynamics
TL;DR: A computational study of the fast marching and the fast sweeping methods for the eikonal equation and fully second order generalizations of methods of this type for problems with obstacles are proposed and implemented. (via Semantic Scholar)
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Added: August 6, 2018

2006 article

On the computation of steady hopper flows III: Model comparisons

Gremaud, P. A., Matthews, J. V., & Schaeffer, D. G. (2006, May 16). Journal of Computational Physics.

By: P. Gremaud n, J. Matthews * & D. Schaeffer*

author keywords: granular; similarity; spectral; plasticity
topics (OpenAlex): Granular flow and fluidized beds; Rheology and Fluid Dynamics Studies; Heat and Mass Transfer in Porous Media
TL;DR: Results indicate that for slow granular flows the lesser known Matsuoka-Nakai plasticity law yields better results than more common models based on a von Mises criterion. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2004 article

Numerical issues in plasticity models for granular materials

Gremaud, P. A. (2004, December 9). Journal of Volcanology and Geothermal Research.

By: P. Gremaud n

author keywords: granular material; plasticity; heap formation; granular flow; numerical methods
topics (OpenAlex): Granular flow and fluidized beds; Geotechnical and Geomechanical Engineering; Fluid Dynamics Simulations and Interactions
Source: Web Of Science
Added: August 6, 2018

2004 article

On the computation of steady Hopper flows

Gremaud, P. A., Matthews, J. V., & O'Malley, M. (2004, June 25). Journal of Computational Physics.

By: P. Gremaud n, J. Matthews * & M. O'Malley n

author keywords: elliptic; granular; similarity; spectral
topics (OpenAlex): Granular flow and fluidized beds; Fluid Dynamics Simulations and Interactions; Fluid Dynamics and Heat Transfer
Source: Web Of Science
Added: August 6, 2018

2004 article

Secondary Circulation in Granular Flow Through Nonaxisymmetric Hoppers

Schaeffer, D. G., Matthews, J. V., & Gremaud, P. A. (2004, January 1). SIAM Journal on Applied Mathematics.

By: D. Schaeffer*, J. Matthews * & P. Gremaud n

author keywords: granular; similarity solution; perturbation theory
topics (OpenAlex): Granular flow and fluidized beds; Lattice Boltzmann Simulation Studies; Fluid Dynamics and Vibration Analysis
TL;DR: This paper uses perturbation theory to compute a first-order correction to the (steady-state) velocity resulting from a small change in hopper geometry, either distortion of the cross section or tilting away from vertical. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2004 article

Volume determination for bulk materials in bunkers

Ahmed, S. A., Buckingham, R., Gremaud, P. A., Hauck, C. D., Kuster, C. M., Prodanovic, M., … Silantyev, V. (2004, October 18). International Journal for Numerical Methods in Engineering.

By: S. Ahmed *, R. Buckingham*, P. Gremaud n, C. Hauck *, C. Kuster n, M. Prodanovic *, T. Royal, V. Silantyev*

author keywords: granular; eikonal formulation; ordered upwind methods
topics (OpenAlex): Geotechnical Engineering and Soil Mechanics; Soil and Unsaturated Flow; Granular flow and fluidized beds
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11. Sustainable Cities and Communities (OpenAlex)
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Added: August 6, 2018

2003 article

Numerical simulation of aerated powder consolidation

Coffey, K. A., & Gremaud, P. A. (2003, January 30). International Journal of Non-Linear Mechanics.

By: K. Coffey n & P. Gremaud n

topics (OpenAlex): Granular flow and fluidized beds; Fluid Dynamics Simulations and Interactions; Numerical methods in engineering
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16. Peace, Justice and Strong Institutions (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2001 article

On a Powder Consolidation Problem

Kelley, C. T., Coffey, K. A., Gremaud, P. A., & Royal, T. A. (2001, January 1). SIAM Journal on Applied Mathematics.

By: C. Kelley n , K. Coffey n, P. Gremaud n & T. Royal

topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Rheology and Fluid Dynamics Studies; Numerical methods for differential equations
TL;DR: A numerical method based on a formulation of the semidiscretized problem as an index 1 DAE is proposed and implemented and the feasibility of the approach is illustrated by computational results. (via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018

2001 article

On the Computation of Steady Hopper Flows

Gremaud, P. A., & Matthews, J. V. (2001, January 1). Journal of Computational Physics.

By: P. Gremaud n & J. Matthews n

author keywords: granular flow; plasticity; hyperbolic conservation laws; discontinuous Galerkin
topics (OpenAlex): Granular flow and fluidized beds; Particle Dynamics in Fluid Flows; Fluid Dynamics and Turbulent Flows
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15. Life on Land (OpenAlex)
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Added: August 6, 2018

2000 article

Numerical determination of flow corrective inserts for granular materials in conical hoppers

Gremaud, P. A., Schaeffer, D. G., & Shearer, M. (2000, September 1). International Journal of Non-Linear Mechanics, Vol. 35, pp. 869–882.

By: P. Gremaud n, D. Schaeffer* & M. Shearer n 

topics (OpenAlex): Granular flow and fluidized beds; Particle Dynamics in Fluid Flows; Geotechnical and Geomechanical Engineering
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 article

Computation of Nonclassical Solutions to Hamilton--Jacobi Problems

Gremaud, P.-A., & Ide, N. R. (1999, January 1). SIAM Journal on Scientific Computing.

By: P. Gremaud* & N. Ide

author keywords: Hamilton-Jacobi; viscosity solution; nonconvex; systems; numerical viscosity
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Navier-Stokes equation solutions; Quantum chaos and dynamical systems
TL;DR: This paper is devoted to the construction of numerical methods for the approximation of nonclassical solutions to multidimensional Hamilton--Jacobi equations for both scalar and vectorial problems, and the convergence of the methods is investigated. (via Semantic Scholar)
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Added: August 6, 2018

1998 article

A Priori Error Estimates for Numerical Methods for Scalar Conservation Laws Part III: Multidimensional Flux-Splitting Monotone Schemes on Non-Cartesian Grids

Cockburn, B., Gremaud, P.-A., & Yang, J. X. (1998, October 1). SIAM Journal on Numerical Analysis.

By: B. Cockburn *, P. Gremaud n & J. Yang*

author keywords: a priori error estimates; irregular grids; monotone schemes; conservation laws; supraconvergence
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Gas Dynamics and Kinetic Theory; Fluid Dynamics and Turbulent Flows
TL;DR: It is shown that nonconsistent schemes can converge at optimal rates of $(\Delta x)^{1/2}$ because the conservation form of the schemes and the so-called consistency of the numerical fluxes allow the regularity properties of the approximate solution to compensate for their lack of consistency. (via Semantic Scholar)
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15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1997 article

A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids

Cockburn, B., & Gremaud, P.-A. (1997, January 1). Mathematics of Computation.

By: B. Cockburn * & P. Gremaud n

author keywords: a priori error estimates; irregular grids; monotone schemes; conservation laws; supraconvergence
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Gas Dynamics and Kinetic Theory; Fluid Dynamics and Turbulent Flows
TL;DR: This paper obtains the optimal rate of convergence of (Δx) 1/2 in L∞(L 1 ) for consistent schemes in arbitrary grids without the use of any regularity property of the approximate solution, and proposes a new explanation of this well-known supraconvergence phenomenon. (via Semantic Scholar)
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15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1997 article

Numerical simulation of pattern formation in grain flows

Gremaud, P.-A. (1997, July 1). Applied Mathematics and Computation.

By: P. Gremaud n

topics (OpenAlex): Lattice Boltzmann Simulation Studies; Granular flow and fluidized beds; Fluid Dynamics and Heat Transfer
Source: Web Of Science
Added: August 6, 2018

1996 article

Error Estimates for Finite Element Methods for Scalar Conservation Laws

Cockburn, B., & Gremaud, P.-A. (1996, April 1). SIAM Journal on Numerical Analysis.

By: B. Cockburn & P. Gremaud n

author keywords: error estimates; streamline diffusion method; discontinuous galerkin method; multidimensional conservation laws
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Fluid Dynamics and Turbulent Flows; Advanced Numerical Methods in Computational Mathematics
TL;DR: New a posteriors error estimates are obtained and these estimates are used to prove that the SCSD method and the SCDG method converge to the entropy solution with a rate of at least $h^{{1 / 8}} $ and $h-norm $, respectively, in the L^\infty (L^1 )-norm. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

1994 article

Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions

Gremaud, P.-A. (1994, February 1). SIAM Journal on Numerical Analysis.

By: P. Gremaud*

author keywords: FINITE ELEMENT METHOD; RATE OF CONVERGENCE; NUMERICAL APPROXIMATION; NONCONVEX; VARIATIONAL PROBLEM
topics (OpenAlex): Shape Memory Alloy Transformations; Topology Optimization in Engineering; Thermoelastic and Magnetoelastic Phenomena
Source: Web Of Science
Added: August 6, 2018

1992 article

Error estimates for Euler forward scheme related to two-phase Stefan problems

Amiez, G., & Gremaud, P.-A. (1992, January 1). ESAIM Mathematical Modelling and Numerical Analysis.

By: G. Amiez* & P. Gremaud*

topics (OpenAlex): Advanced Mathematical Modeling in Engineering; Differential Equations and Numerical Methods; Advanced Numerical Methods in Computational Mathematics
Source: Web Of Science
Added: August 6, 2018

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