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Jan Sickmann Hesthaven

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Related publications (102)

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Machine-Learning-Enhanced Real-Time Aerodynamic Forces Prediction Based on Sparse Pressure Sensor Inputs

Jan Sickmann Hesthaven, Junming Duan

Accurate real-time prediction of aerodynamic forces is crucial for the navigation of unmanned aerial vehicles (UAVs). This paper presents a data-driven aerodynamic force prediction model based on a small number of pressure sensors located on the surface of ...

2024

A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

Jan Sickmann Hesthaven

For two-dimensional (2D) time fractional diffusion equations, we construct a numerical method based on a local discontinuous Galerkin (LDG) method in space and a finite difference scheme in time. We investigate the numerical stability and convergence of th ...

SPRINGERNATURE2020

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2022

Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks

Jan Sickmann Hesthaven, Mariella Kast

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time -dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the ...

2024

Modeling synchronization in globally coupled oscillatory systems using model order reduction

Jan Sickmann Hesthaven, Niccolo' Discacciati

We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suita ...

American Institute of Physics2021

Rare event simulation for large-scale structures with local nonlinearities

Jan Sickmann Hesthaven, Zhenying Zhang

ELSEVIER SCIENCE SA2020

On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method

Jan Sickmann Hesthaven

We propose a modified parallel-in-time - parareal-multi-level time integration method that, in contrast to previously proposed methods, employs a coarse solver based on a reduced model, built from the information obtained from the fine solver at each itera ...

Springer Int Publishing Ag2014

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

Jan Sickmann Hesthaven, Deep Ray, Lukas Schwander

While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution r ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study

Jan Sickmann Hesthaven

A potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the man-made groundwater reservoir is modeled as a coupled poroviscoelastic–viscoelastic medium, and the underly ...

2024

Time domain room acoustic simulations using the spectral element method

Jan Sickmann Hesthaven

This paper presents a wave-based numerical scheme based on a spectral element method, coupled with an implicit-explicit Runge-Kutta time stepping method, for simulating room acoustics in the time domain. The scheme has certain features which make it highly ...

ACOUSTICAL SOC AMER AMER INST PHYSICS2019

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a model order reduction technique to accurately approximate the behavior of multi-component systems without any a-priori knowledge of the coupled model. In the offline phase, we construct independent surrogate models by solving the local problem ...

Wiley2023

A data-driven shock capturing approach for discontinuous Galekin methods

Jan Sickmann Hesthaven

We propose a data-driven artificial viscosity model for shock capturing in discontinuous Galerkin methods. The proposed model trains a multi-layer feedforward network to map from the element-wise solution to a smoothness indicator, based on which the artif ...

2022

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

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Jan Sickmann Hesthaven, Cecilia Pagliantini, Nicolò Ripamonti

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

EDP SCIENCES S A2022

Local discontinuous Galerkin methods for fractional ordinary differential equations

Jan Sickmann Hesthaven

This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of the numerical fluxes for the initial value problem for FODEs ensures stabili ...

2015

A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Jan Sickmann Hesthaven, Mengwu Guo, Mariella Kast

We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial differential equations (PDEs) that leverages models of different accuracy. From a collection of low-fidelity (LF) snapshots, parameter locations are extracted for the e ...

ELSEVIER SCIENCE SA2020

Two-Dimensional RBF-ENO Method on Unstructured Grids

Jan Sickmann Hesthaven, Fabian Mönkeberg

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well stud ...

SPRINGER/PLENUM PUBLISHERS2020

Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

Jan Sickmann Hesthaven, Paolo Gatto

We previously introduced a preconditioner that has proven effective for hp-FEM dis- cretizations of various challenging elliptic and hyperbolic problems. The construc- tion is inspired by standard nested dissection, and relies on the assumption that the Sc ...

Elsevier2017

A new variable shape parameter strategy for RBF approximation using neural networks

Jan Sickmann Hesthaven

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate ho ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

Jan Sickmann Hesthaven, Benjamin Stamm

We propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment ...

EDP Sciences2014