Jan Sickmann Hesthaven

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A non-intrusive reduced order model (ROM) that combines a proper orthogonal decomposition (POD) and an artificial neural network (ANN) is primarily studied to investigate the applicability of the proposed ROM in recovering the solutions with shocks and str ...

We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order alpha [1,2] defined through the fractional Laplacian. The fractional operator of order alpha is expressed as a composite of first order der ...

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precisi ...

This paper presents a fast direct solver for the Combined Field Integral Equation using higher-order discretizations. By adopting higher-order polynomials with the Method of Moments, the number of unknowns is significantly reduced. The fast direct solver l ...

The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...

We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by examining the Bhatnagar-Gross-Krook (BGK) approximation and using the perfectly matched layer (PML) technique. To ensure stability, we discard some parameters in the ...

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 ...

Discontinuous Galerkin (DG) method is presented for numerical modeling of melt migration in a chemically reactive and viscously deforming upwelling mantle column. DG methods for both advection and elliptic equations provide a robust and efficient solution ...

The discontinuous Galerkin method is used to solve the non-linear spherical shallow water equations with Coriolis force. The numerical method is well-balanced and takes wetting/drying into account. The two fold goal of this work is a comparative study of d ...

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 ...

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 ...

Fluorescence Image Guided Surgery utilizes continuous wave epi-fluorescence measurements on the tissue surface to locate targets such as tumors or lymph nodes, but precise 3D localization of deep targets remains intractable due to the illposedness of the a ...

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 ...

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the concept of feed ...

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 ...

In this paper we consider some practical applications of model reduction methods in unstable gas turbine and rocket combustion. We explore a set of promising methods for reducing computational burden in large scale LES calculations of unsteady turbulent co ...

In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwell's equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for ...

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 ...

Jan Sickmann Hesthaven

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Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability

Discontinuous Galerkin method for fractional convection-diffusion equations

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

A Fast Direct Solver for Higher Order Discretizations of Integral Equations

An Adjoint Approach for Stabilizing the Parareal Method

Perfectly matched layers for the Boltzmann equation: Stability and sensitivity analysis

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics

A comparative study of earthquake source models in high- order accurate tsunami simulations

An artificial neural network as a troubled-cell indicator

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

Leveraging Contrast Agent Kinetics for Robust Reflectance Mode Fluorescence Tomography

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

GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications

Hyperbolic Problems: Theory and Computation

Flowfield Reconstruction Method Using Artificial Neural Network

Applications of Model Reduction Techniques in Aerospace Combustors

Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

Preface to Focused Issue on Discontinuous Galerkin Methods PREFACE

Conservative Model Order Reduction for Fluid Flow