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Jan Sickmann Hesthaven

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

Jan Sickmann Hesthaven, Cecilia Pagliantini

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

2018

Conservative Model Order Reduction for Fluid Flow

Qian Wang, Jan Sickmann Hesthaven, Nicolò Ripamonti, Babak Maboudi Afkham

In the past decade, model order reduction (MOR) has been successful in reducing the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. Symmetries an ...

Springer Verlag2018

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

Symplectic Model-Reduction with a Weighted Inner Product

Jan Sickmann Hesthaven, Babak Maboudi Afkham

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

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

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

A nodal discontinuous Galerkin finite element method for the poroelastic wave equation

Jan Sickmann Hesthaven, Khemraj Shukla

We use the nodal discontinuous Galerkin method with a Lax-Friedrich flux to model the wave propagation in transversely isotropic and poroelastic media. The effect of dissipation due to global fluid flow causes a stiff relaxation term, which is incorporated ...

2018

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

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

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Reduced order modeling for nonlinear structural analysis using Gaussian process regression

Jan Sickmann Hesthaven, Mengwu Guo

2018

Conservative Model Order Reduction for Fluid Flow

Qian Wang, Jan Sickmann Hesthaven, Nicolò Ripamonti, Babak Maboudi Afkham

Springer Verlag2018

2018

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

Jan Sickmann Hesthaven

Stefano Ubbiali

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

2018