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Jan Sickmann Hesthaven

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Publications associées (102)

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Babak Maboudi Afkham, Jan Sickmann Hesthaven

Reduced basis methods are popular for approximately solving large and complex systems of dierential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model. Here, we present ...

2019

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Jan Sickmann Hesthaven, Mengwu Guo

A non-intrusive reduced basis (RB) method is proposed for parametrized nonlinear structural analysis undergoing large deformations and with elasto-plastic constitutive relations. In this method, a reduced basis is constructed from a set of full-order snaps ...

2018

An artificial neural network as a troubled-cell indicator

Jan Sickmann Hesthaven, Deep Ray

High-resolution schemes for conservation laws need to suitably limit the numerical solution near discontinuities, in order to avoid Gibbs oscillations. The solution quality and the computational cost of such schemes strongly depend on their ability to corr ...

2018

Non-intrusive reduced order modeling of nonlinear problems using neural networks

Jan Sickmann Hesthaven, Stefano Ubbiali

We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and emplo ...

2018

Detecting troubled-cells on two-dimensional unstructured grids using a neural network

Jan Sickmann Hesthaven, Deep Ray

In a recent paper [Ray and Hesthaven, J. Comput. Phys. 367 (2018), pp 166-191], we proposed a new type of troubled-cell indicator to detect discontinuities in the numerical solutions of one-dimensional conservation laws. This was achieved by suitably train ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2018

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

Cecilia Pagliantini, Jan Sickmann Hesthaven

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

2018

Symplectic Model-Reduction with a Weighted Inner Product

Babak Maboudi Afkham, Jan Sickmann Hesthaven

In the recent years, considerable attention has been paid to preserving structures and invariants in reduced basis methods, in order to enhance the stability and robustness of the reduced system. In the context of Hamiltonian systems, symplectic model redu ...

2018

Data-driven reduced order modeling for time-dependent problems

Jan Sickmann Hesthaven, Mengwu Guo

A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order ...

2018

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

Qian Wang, Jan Sickmann Hesthaven, Deep Ray

A non-intrusive reduced-basis (RB) method is proposed for parametrized unsteady flows. A set of reduced basis functions are extracted from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD), and the coefficients of the redu ...

2018

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

Jan Sickmann Hesthaven, Boris Bonev

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

2018

Flowfield Reconstruction Method Using Artificial Neural Network

Jan Sickmann Hesthaven

Multi-dimensional aerodynamic database development has become more and more impor- tant for the design, control and guidance of modern aircrafts. In order to relieve the curse of the dimensionality, we propose a novel flow field reconstruction method based ...

2018

Identification of a Predator-Prey System from Simulation Data of a Convection Model

Jan Sickmann Hesthaven

The use of low-dimensional dynamical systems as reduced models for plasma dynamics is useful as solving an initial value problem requires much less computational resources than fluid simulations. We utilize a data-driven modeling approach to identify a red ...

American Institute of Physics2017

High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our stud ...

Springer Verlag2017

A comparative study of shock capturing models for the discontinuous Galerkin method

Jan Sickmann Hesthaven

Dealing with strong shocks while retaining numerical dissipation of reasonably low level has been one of the major challenges for high order methods like discontinuous Galerkin. In the literature, various shock capturing models have been designed based on ...

Elsevier2017

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations

Gilles Brunner, Jan Sickmann Hesthaven, Allan Svejstrup Nielsen

In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyon ...

2017

High-Order Accurate Local Schemes for Fractional Differential Equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

High-order methods inspired by the multi-step Adams methods are proposed for systems of fractional differential equations. The schemes are based on an expansion in a weighted space. To obtain the schemes this expansion is terminated after terms. We study t ...

Springer Verlag2017

Structure preserving model reduction of parametric Hamiltonian systems

Babak Maboudi Afkham, Jan Sickmann Hesthaven

While reduced-order models (ROMs) are popular for approximately solving large systems of differential equations, the stability of reduced models over long-time integration remains an open question. We present a greedy approach for ROM generation of paramet ...

2017

Adaptive WENO methods based on radial basis functions reconstruction

Jan Sickmann Hesthaven, Caterina Bigoni

We explore the use of radial basis functions (RBF) in the weighted essentially non-oscillatory (WENO) reconstruction process used to solve hyperbolic conservation laws, resulting in a numerical method of arbitrarily high order to solve problems with discon ...

Springer Verlag2017

A kernel compression scheme for fractional differential equations

Jan Sickmann Hesthaven, Daniel Henri Baffet

The nonlocal nature of the fractional integral makes the numerical treatment of fractional dierential equations expensive in terms of computational eort and memory requirements. In this paper we propose a method to reduce these costs while controlling the ...

Society for Industrial and Applied Mathematics2017

A greedy non-intrusive reduced order model for fluid dynamics

Jan Sickmann Hesthaven

We introduce a greedy non-intrusive reduced order method(ROM) for parameterized time-dependent problems with an emphasis on problems in fluid dynamics. The non-intrusive ROM is based on two-level proper orthogonal decomposition(POD) to extract temporal and ...

American Institute of Aeronautics and Astronautics2017

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