The research activities focuses on the development, analysis and application of high-order accurate computational methods for time-dependent partial differential equations with a particular emphasis on linear and nonlinear wave problems. This has and continues to included research activities in discontinuous Galerkin and spectral methods, certificed reduced basis methods, methods for uncertainty quantification, methods for multiscale problems in time and space, efficient multilevel solvers and fractional differential equations. A major recent activity is the use of machine learning techniques in computational science with an emphasis on methods that preserve physical characteristics or the use of local neural networks to accelerate existing methods rather than replacing them.
While the emphasis in on the development and analysis of new methods and algorithms, the research is application driven and we generally maintain a strong focus on tying the theoretical developments to real applications, ranging from electromagnetics and plasma physics to geoscience and combustion. There is also a sustained interest in the development of methods and algorithms for parallel computing, GPU accelerated computing and the development of resilient algorithms, to support the development and use of large scale computational tool to enable predictive similation science.
Jan S Hesthaven publications
M. Kast; M. Guo; J. S. Hesthaven : A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems; Computer Methods In Applied Mechanics And Engineering. 2020-06-01. DOI : 10.1016/j.cma.2020.112947.
N. Discacciati; J. S. Hesthaven; D. Ray : Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks; Journal Of Computational Physics. 2020-05-15. DOI : 10.1016/j.jcp.2020.109304.
C. Bigoni; J. S. Hesthaven : Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring; Computer Methods In Applied Mechanics And Engineering. 2020-05-01. DOI : 10.1016/j.cma.2020.112896.
J. Yu; J. S. Hesthaven : A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework; Communications In Computational Physics. 2020-05-01. DOI : 10.4208/cicp.OA-2019-0118.
Q. Wang; N. Ripamonti; J. S. Hesthaven : Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism; Journal of Computational Physics. 2020-03-14. DOI : 10.1016/j.jcp.2020.109402.
W. Hao; J. Hesthaven; G. Lin; B. Zheng : A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations; Journal Of Scientific Computing. 2020-01-13. DOI : 10.1007/s10915-020-01123-1.
K. Shukla; J. M. Carcione; J. S. Hesthaven; E. L'heureux : Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method. 2019-12-23.
Q. Wang; N. Ripamonti; J. S. Hesthaven : Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism; Journal of Computational Physics. 2019-08-18.
Z. Zhang; M. Guo; J. S. Hesthaven : Model order reduction for large-scale structures with local nonlinearities; Computer Methods In Applied Mechanics and Engineering. 2019-08-15. DOI : 10.1016/j.cma.2019.04.042.
M. Hajihassanpour; B. Bonev; J. S. Hesthaven : A comparative study of earthquake source models in high- order accurate tsunami simulations; Ocean Modelling. 2019-08-14. DOI : 10.1016/j.ocemod.2019.101429.
J. S. Hesthaven; F. Monkeberg : Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction; ESAIM: Mathematical Modelling and Numerical Analysis. 2019-06-21. DOI : 10.1051/m2an/2019011.
F. Pind; A. P. Engsig-Karup; C.-H. Jeong; J. S. Hesthaven; M. S. Mejling et al. : Time domain room acoustic simulations using the spectral element method; Journal Of The Acoustical Society Of America. 2019-06-01. DOI : 10.1121/1.5109396.
N. Discacciati; J. S. Hesthaven; D. Ray : MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks. 2019-01-28.
T. Lahivaara; A. Pasanen; L. Karkkainen; J. M. Huttunen; J. S. Hesthaven et al. : Estimation of groundwater storage from seismic data using deep learning; Geophysics Research Letters. 2019. DOI : 10.1111/1365-2478.12831.
A. Karakus; N. Chalmers; J. S. Hesthaven; T. Warburton : Discontinuous Galerkin Discretizations of the Boltzmann Equations in 2D: semi-analytic time stepping and absorbing boundary layers; Journal of Computational Physics. 2019. DOI : 10.1016/j.jcp.2019.03.050.
Q. Wang; J. S. Hesthaven; D. Ray : Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem; Journal of Computational Physics. 2018-06-18. DOI : 10.1016/j.jcp.2019.01.031.
K. Shukla; J. S. Hesthaven; J. M. Carcione; R. Ye; J. de la Puenta et al. : A nodal discontinuous Galerkin finite element method for the poroelastic wave equation; Computational Geoscience. 2018. DOI : 10.1007/s10596-019-9809-1.
M. Guo; J. S. Hesthaven : Reduced order modeling for nonlinear structural analysis using Gaussian process regression; Computer Methods in Applied Mechanics and Engineering. 2018. DOI : 10.1016/j.cma.2018.07.017.
B. Bonev; J. S. Hesthaven; F. X. Giraldo; M. A. Kopera : Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction; Journal of Computational Physics. 2018. DOI : 10.1016/j.jcp.2018.02.008.
T. Lahivaara; L. Karkkainen; J. M. Huttunen; J. S. Hesthaven : Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography; Journal of the Acoustical Society of America. 2018. DOI : 10.1121/1.5024341.
A. S. Nielsen; G. Brunner; J. S. Hesthaven : Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations; Journal of Computational Physics. 2017. DOI : 10.1016/j.jcp.2018.04.056.
P. Gatto; J. S. Hesthaven; R. Christiansen : Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization; Computer Methods in Applied Mechanics and Engineering. 2017. DOI : 10.1016/j.cma.2017.04.027.
D. H. Baffet; J. S. Hesthaven : High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations; Journal of Scientific Computing. 2017. DOI : 10.1007/s10915-017-0393-z.
S. Yeganeh; R. Mokhtari; J. S. Hesthaven : Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method; BIT Numerical Mathematics. 2017. DOI : 10.1007/s10543-017-0648-y.
D. Forti / A. Quarteroni; S. Deparis (Dir.) : Parallel Algorithms for the Solution of Large-Scale Fluid-Structure Interaction Problems in Hemodynamics. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6983.
J. S. Hesthaven; S. Zhang : On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations; Journal of Scientific Computing. 2016. DOI : 10.1007/s10915-016-0194-9.
F. Chen; J. S. Hesthaven; Y. Maday; A. S. Nielsen : An Adjoint Approach for Stabilizing the Parareal Method; Comptes rendus des séances de l'Académie des Sciences. Série A, Sciences mathématiques**. 2015.
J. Zudrop; J. S. Hesthaven : Accuracy of high order and spectral methods for hyperbolic conservation laws with discontinuous solutions; Siam Journal on Numerical Analysis. 2015. DOI : 10.1137/140992758.
L. Qiu; W. Deng; J. S. Hesthaven : Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes; Journal of Computational Physics. 2015. DOI : 10.1016/j.jcp.2015.06.022.
F. Nobile; L. Tamellini; R. Tempone : Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs. 2015. International Conference on Spectral and High-Order Methods 2014 (ICOSAHOM'14), Salt Lake City, June 23-27, 2014. p. 475-482. DOI : 10.1007/978-3-319-19800-2_44.
P. Gatto; J. S. Hesthaven : Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising; Journal of Scientific Computing. 2015. DOI : 10.1007/s10915-014-9959-1.
S. Tirupathi; J. S. Hesthaven; Y. Liang; M. Parmentier : Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics; Computational Geosciences. 2015. DOI : 10.1007/s10596-015-9514-7.
F. Chen; J. S. Hesthaven; X. Zhu : On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method. 2014. Workshop on Reduced Basis, POD and Reduced Order Methods for Model and Computational Reduction: towards Real-time Computing and Visualization', Lausanne, CH. p. 187-214. DOI : 10.1007/978-3-319-02090-7_7.
J. Li; J. S. Hesthaven : Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials; Journal Of Computational Physics. 2014. DOI : 10.1016/j.jcp.2013.11.018.