A Stable Penalty Method for the Compressible Navier-Stokes Equations: I. Open Boundary Conditions. - Jan S. Hesthaven; David I. Gottlieb (SIAM J. Sci. Comput., 1996)

A Stable Penalty Method for the Compressible Navier-Stokes Equations: II. One-Dimensional Domain Decomposition Schemes. - Jan S. Hesthaven (SIAM J. Sci. Comput., 1997)

A Stable Penalty Method for the Compressible Navier-Stokes Equations: III. Multidimensional Domain Decomposition Schemes. - Jan S. Hesthaven (SIAM J. Sci. Comput., 1998)

Stable Spectral Methods on Tetrahedral Elements. - Jan S. Hesthaven; C. H. Teng (SIAM J. Sci. Comput., 2000)

Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems. - I. Fatkullin; Jan S. Hesthaven (J. Sci. Comput., 2001)

Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics. - Saul Abarbanel; David I. Gottlieb; Jan S. Hesthaven (J. Sci. Comput., 2002)

Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media. - Guo-Xin Fan; Qing Huo Liu; Jan S. Hesthaven (IEEE Trans. Geosci. Remote. Sens., 2002)

Foreword. - Mark H. Carpenter; David I. Gottlieb; Jan S. Hesthaven; Chi-Wang Shu (J. Sci. Comput., 2005)

Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs. - Qian-Yong Chen; David I. Gottlieb; Jan S. Hesthaven (SIAM J. Numer. Anal., 2005)

High-Order Collocation Methods for Differential Equations with Random Inputs. - Dongbin Xiu; Jan S. Hesthaven (SIAM J. Sci. Comput., 2005)

High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids. - Gustaaf B. Jacobs; Jan S. Hesthaven (J. Comput. Phys., 2006)

Idempotent filtering in spectral and spectral element methods. - Alex Kanevsky; Mark H. Carpenter; Jan S. Hesthaven (J. Comput. Phys., 2006)

Non-Linear PML Equations for Time Dependent Electromagnetics in Three Dimensions. - Saul Abarbanel; David I. Gottlieb; Jan S. Hesthaven (J. Sci. Comput., 2006)

Foreword. - David I. Gottlieb; Jan S. Hesthaven; George E. Karniadakis; Chi-Wang Shu (J. Sci. Comput., 2006)

Padé-Legendre Interpolants for Gibbs Reconstruction. - Jan S. Hesthaven; Sidi Mahmoud Kaber; Laura B. Lurati (J. Sci. Comput., 2006)

Computational Modeling of Uncertainty in Time-Domain Electromagnetics. - Cédric Chauvière; Jan S. Hesthaven; Laura B. Lurati (SIAM J. Sci. Comput., 2006)

Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes. - Alex Kanevsky; Mark H. Carpenter; David I. Gottlieb; Jan S. Hesthaven (J. Comput. Phys., 2007)

Filtering in Legendre spectral methods. - Jan S. Hesthaven; Robert M. Kirby (Math. Comput., 2008)

Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning. - Gustaaf B. Jacobs; Jan S. Hesthaven (Comput. Phys. Commun., 2009)

High-order accurate thin layer approximations for time-domain electromagnetics. Part I: General metal backed coatings. - Sehun Chun; Jan S. Hesthaven (J. Comput. Appl. Math., 2009)

Polymorphic nodal elements and their application in discontinuous Galerkin methods. - Gregor Gassner; Frieder Lörcher; Claus-Dieter Munz; Jan S. Hesthaven (J. Comput. Phys., 2009)

Nodal discontinuous Galerkin methods on graphics processors. - Andreas Klöckner; Tim Warburton; Jeff Bridge; Jan S. Hesthaven (J. Comput. Phys., 2009)

On ANOVA expansions and strategies for choosing the anchor point. - Zhen Gao 002; Jan S. Hesthaven (Appl. Math. Comput., 2010)

High-order accurate thin layer approximations for time-domain electromagnetics, Part II: Transmission layers. - Sehun Chun; Houssem Haddar; Jan S. Hesthaven (J. Comput. Appl. Math., 2010)

Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations. - Yanlai Chen; Jan S. Hesthaven; Yvon Maday; Jerónimo Rodríguez (SIAM J. Sci. Comput., 2010)

The reduced basis method for the electric field integral equation. - M. Fares; Jan S. Hesthaven; Yvon Maday; Benjamin Stamm (J. Comput. Phys., 2011)

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws. - Khosro Shahbazi; Nathan Albin; Oscar P. Bruno; Jan S. Hesthaven (J. Comput. Phys., 2011)

A generalization of the Wiener rational basis functions on infinite intervals: Part I-derivation and properties. - Akil Narayan 001; Jan S. Hesthaven (Math. Comput., 2011)

High-Order Discontinuous Galerkin Methods by GPU Metaprogramming - Andreas Klöckner; Timothy Warburton; Jan S. Hesthaven (CoRR, 2012)

A reduced basis method for electromagnetic scattering by multiple particles in three dimensions. - Mahadevan Ganesh; Jan S. Hesthaven; Benjamin Stamm (J. Comput. Phys., 2012)

Certified Reduced Basis Method for the Electric Field Integral Equation. - Jan S. Hesthaven; Benjamin Stamm; S. Zhang (SIAM J. Sci. Comput., 2012)

Fast prediction and evaluation of gravitational waveforms using surrogate models. - Scott E. Field; Chad R. Galley; Jan S. Hesthaven; Jason Kaye; Manuel Tiglio (CoRR, 2013)

Solving Wave Equations on Unstructured Geometries - Andreas Klöckner; Timothy Warburton; Jan S. Hesthaven (CoRR, 2013)

A generalization of the Wiener rational basis functions on infinite intervals, Part II - Numerical investigation. - Akil C. Narayan; Jan S. Hesthaven (J. Comput. Appl. Math., 2013)

Multi-dimensional hybrid Fourier continuation-WENO solvers for conservation laws. - Khosro Shahbazi; Jan S. Hesthaven; Xueyu Zhu (J. Comput. Phys., 2013)

Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials. - Jichun Li 001; Jan S. Hesthaven (J. Comput. Phys., 2014)

Stable multi-domain spectral penalty methods for fractional partial differential equations. - Qinwu Xu; Jan S. Hesthaven (J. Comput. Phys., 2014)

High-Order Multiscale Finite Element Method for Elliptic Problems. - Jan S. Hesthaven; Shun Zhang 001; Xueyu Zhu (Multiscale Model. Simul., 2014)

Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations. - Qinwu Xu; Jan S. Hesthaven (SIAM J. Numer. Anal., 2014)

A multi-domain spectral method for time-fractional differential equations. - Feng Chen 019; Qinwu Xu; Jan S. Hesthaven (J. Comput. Phys., 2015)

Special Issue on "Fractional PDEs: Theory, Numerics, and Applications". - George E. Karniadakis; Jan S. Hesthaven; Igor Podlubny (J. Comput. Phys., 2015)

Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes. - Liangliang Qiu; Weihua Deng; Jan S. Hesthaven (J. Comput. Phys., 2015)

A parareal method for time-fractional differential equations. - Qinwu Xu; Jan S. Hesthaven; Feng Chen 019 (J. Comput. Phys., 2015)

Numerical Approximation of the Fractional Laplacian via hp-finite Elements, with an Application to Image Denoising. - Paolo Gatto; Jan S. Hesthaven (J. Sci. Comput., 2015)

Hyperbolic Problems: Theory and Computation. - Jan S. Hesthaven; Jae-Hun Jung; Allen M. Tesdall (J. Sci. Comput., 2015)

Reduced Basis Multiscale Finite Element Methods for Elliptic Problems. - Jan S. Hesthaven; Shun Zhang 001; Xueyu Zhu (Multiscale Model. Simul., 2015)

Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions. - Jens Zudrop; Jan S. Hesthaven (SIAM J. Numer. Anal., 2015)

Fault Tolerance in the Parareal Method. - Allan S. Nielsen; Jan S. Hesthaven (FTXS@HPDC, 2016)

Research and Education in Computational Science and Engineering. - Ulrich Rüde; Karen Willcox; Lois Curfman McInnes; Hans De Sterck; George Biros; Hans-Joachim Bungartz; James Corones; Evin Cramer; James Crowley; Omar Ghattas; Max D. Gunzburger; Michael Hanke; et al. (CoRR, 2016)

On the Use of ANOVA Expansions in Reduced Basis Methods for Parametric Partial Differential Equations. - Jan S. Hesthaven; Shun Zhang 001 (J. Sci. Comput., 2016)

High-Order Accurate Local Schemes for Fractional Differential Equations. - Daniel Baffet; Jan S. Hesthaven (J. Sci. Comput., 2017)

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations. - Daniel Baffet; Jan S. Hesthaven (J. Sci. Comput., 2017)

Adaptive WENO Methods Based on Radial Basis Function Reconstruction. - Caterina Bigoni; Jan S. Hesthaven (J. Sci. Comput., 2017)

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations. - Paolo Gatto; Jan S. Hesthaven (J. Sci. Comput., 2017)

A Kernel Compression Scheme for Fractional Differential Equations. - Daniel Baffet; Jan S. Hesthaven (SIAM J. Numer. Anal., 2017)

Structure Preserving Model Reduction of Parametric Hamiltonian Systems. - Babak Maboudi Afkham; Jan S. Hesthaven (SIAM J. Sci. Comput., 2017)

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction. - Boris Bonev; Jan S. Hesthaven; Francis X. Giraldo; Michal A. Kopera (J. Comput. Phys., 2018)

Non-intrusive reduced order modeling of nonlinear problems using neural networks. - Jan S. Hesthaven; Stefano Ubbiali (J. Comput. Phys., 2018)

Communication-aware adaptive Parareal with application to a nonlinear hyperbolic system of partial differential equations. - Allan S. Nielsen; Gilles Brunner; Jan S. Hesthaven (J. Comput. Phys., 2018)

An artificial neural network as a troubled-cell indicator. - Deep Ray; Jan S. Hesthaven (J. Comput. Phys., 2018)

Projective multiscale time-integration for electrostatic particle-in-cell methods. - Paul Cazeaux; Jan S. Hesthaven (Comput. Phys. Commun., 2019)

Discontinuous Galerkin discretizations of the Boltzmann-BGK equations for nearly incompressible flows: Semi-analytic time stepping and absorbing boundary layers. - Ali Karakus; Noel Chalmers; Jan S. Hesthaven; Tim Warburton (J. Comput. Phys., 2019)

Detecting troubled-cells on two-dimensional unstructured grids using a neural network. - Deep Ray; Jan S. Hesthaven (J. Comput. Phys., 2019)

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem. - Qian Wang 021; Jan S. Hesthaven; Deep Ray (J. Comput. Phys., 2019)

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems. - Babak Maboudi Afkham; Jan S. Hesthaven (J. Sci. Comput., 2019)

Rank-adaptive structure-preserving reduced basis methods for Hamiltonian systems. - Jan S. Hesthaven; Cecilia Pagliantini; Nicolò Ripamonti (CoRR, 2020)

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks. - Niccolò Discacciati; Jan S. Hesthaven; Deep Ray (J. Comput. Phys., 2020)

Constraint-aware neural networks for Riemann problems. - Jim Magiera; Deep Ray; Jan S. Hesthaven; Christian Rohde (J. Comput. Phys., 2020)

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism. - Qian Wang 021; Nicolò Ripamonti; Jan S. Hesthaven (J. Comput. Phys., 2020)

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations. - Wenrui Hao; Jan S. Hesthaven; Guang Lin 001; Bin Zheng (J. Sci. Comput., 2020)

Two-Dimensional RBF-ENO Method on Unstructured Grids. - Jan S. Hesthaven; Fabian Mönkeberg (J. Sci. Comput., 2020)

An Edge Detector Based on Artificial Neural Network with Application to Hybrid Compact-WENO Finite Difference Scheme. - Xiao Wen; Wai Sun Don; Zhen Gao 002; Jan S. Hesthaven (J. Sci. Comput., 2020)

Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation. - Qifeng Zhang; Jan S. Hesthaven; Zhi-Zhong Sun; Yunzhu Ren (Adv. Comput. Math., 2021)

Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities. - Mengwu Guo; Andrea Manzoni; Maurice Amendt; Paolo Conti; Jan S. Hesthaven (CoRR, 2021)

Efficient numerical room acoustic simulations with parametrized boundaries using the spectral element and reduced basis method. - Hermes Sampedro Llopis; Allan P. Engsig-Karup; Cheol-Ho Jeong; Finnur Pind; Jan S. Hesthaven (CoRR, 2021)

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics. - Federico Pichi; Francesco Ballarin; Gianluigi Rozza; Jan S. Hesthaven (CoRR, 2021)

Structure-preserving model order reduction of Hamiltonian systems. - Jan S. Hesthaven; Cecilia Pagliantini; Nicolò Ripamonti (CoRR, 2021)

Physics-informed machine learning for reduced-order modeling of nonlinear problems. - Wenqian Chen; Qian Wang 021; Jan S. Hesthaven; Chuhua Zhang (J. Comput. Phys., 2021)

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks. - Lukas Schwander; Deep Ray; Jan S. Hesthaven (J. Comput. Phys., 2021)

Hybrid high-resolution RBF-ENO method. - Jan S. Hesthaven; Fabian Mönkeberg (J. Comput. Phys. X, 2021)

Structure-preserving reduced basis methods for Poisson systems. - Jan S. Hesthaven; Cecilia Pagliantini (Math. Comput., 2021)

Multi-fidelity surrogate modeling using long short-term memory networks. - Paolo Conti; Mengwu Guo; Andrea Manzoni; Jan S. Hesthaven (CoRR, 2022)

Model order reduction for compressible flows solved using the discontinuous Galerkin methods. - Jian Yu; Jan S. Hesthaven (J. Comput. Phys., 2022)

FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment. - Oscar P. Bruno; Jan S. Hesthaven; Daniel V. Leibovici (J. Comput. Phys. X, 2022)

Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks. - Przemyslaw Zielinski; Jan S. Hesthaven (J. Nonlinear Sci., 2022)

A Hierarchical Preconditioner for Wave Problems in Quasilinear Complexity. - Boris Bonev; Jan S. Hesthaven (SIAM J. Sci. Comput., 2022)

Reduced basis methods for time-dependent problems. - Jan S. Hesthaven; Cecilia Pagliantini; Gianluigi Rozza (Acta Numer., 2022)

A new variable shape parameter strategy for RBF approximation using neural networks. - Fatemeh Nassajian Mojarrad; Maria Han Veiga; Jan S. Hesthaven; Philipp Öffner (Comput. Math. Appl., 2023)

Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs. - Junming Duan; Qian Wang 021; Jan S. Hesthaven (CoRR, 2023)

Adaptive symplectic model order reduction of parametric particle-based Vlasov-Poisson equation. - Jan S. Hesthaven; Cecilia Pagliantini; Nicolò Ripamonti (Math. Comput., 2023)

Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction. - Nicola Rares Franco; Andrea Manzoni; Paolo Zunino; Jan S. Hesthaven (CoRR, 2024)

Fast Numerical Approximation of Linear, Second-Order Hyperbolic Problems Using Model Order Reduction and the Laplace Transform. - Fernando Henríquez; Jan S. Hesthaven (CoRR, 2024)

Neural empirical interpolation method for nonlinear model reduction. - Max Hirsch; Federico Pichi; Jan S. Hesthaven (CoRR, 2024)

GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications. - Oisín M. Morrison; Federico Pichi; Jan S. Hesthaven (CoRR, 2024)

Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems. - Matteo Caldana; Jan S. Hesthaven (CoRR, 2024)

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics. - Anders Melander; Emil Strøm; Finnur Pind; Allan P. Engsig-Karup; Cheol-Ho Jeong; Tim Warburton; Noel Chalmers; Jan S. Hesthaven (Int. J. High Perform. Comput. Appl., 2024)

Positional embeddings for solving PDEs with evolutional deep neural networks. - Mariella Kast; Jan S. Hesthaven (J. Comput. Phys., 2024)

Perfectly matched layers for the Boltzmann equation: Stability and sensitivity analysis. - Marco Sutti; Jan S. Hesthaven (J. Comput. Phys., 2024)

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems. - Junming Duan; Jan S. Hesthaven (J. Comput. Phys., 2024)

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs. - Federico Pichi; Beatriz Moya; Jan S. Hesthaven (J. Comput. Phys., 2024)

Leveraging Contrast Agent Kinetics for Robust Reflectance Mode Fluorescence Tomography. - Mariella Kast; Mykhaylo Zayats; Shayan Shafiee; Sergiy Zhuk; Jan S. Hesthaven; Amit Joshi (ISBI, 2025)

A coordinate transformation-based physics-informed neural networks for hyperbolic conservation laws. - Yuanhong Chen; Zhen Gao 002; Jan S. Hesthaven; Yifan Lin; Xiang Sun (J. Comput. Phys., 2025)

Galerkin neural network-POD for acoustic and electromagnetic wave propagation in parametric domains. - Philipp Weder; Mariella Kast; Fernando Henríquez; Jan S. Hesthaven (Adv. Comput. Math., 2025)