Jan Sickmann Hesthaven

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The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...

Seeking to develop efficient and accurate absorbing layers for the low-speed weakly compressible Navier-Stokes equations, we exploit the connection to the BGK-approximation to develop an absorbing layer with qualities similar to that of the perfectly match ...

The simulation of problems in kinetic plasma physics is often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of Equation-Free Projective ...

A projection-based reduced order model (ROM) based on the Fourier collocation method is proposed for compressible flows. The incorporation of localized artificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM fo ...

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 ...

A fit-for-purpose structural and statistical model is the first major requirement in population pharmacometric model development. In this manuscript we discuss how this complex and computationally intensive task could benefit from supervised machine learni ...

Neural networks provide an attractive framework to monitor the water table level and the volume of stored water in porous media from seismic data in an automated, fast and cost-efficient manner. In this work, a subsurface reservoir is modeled as a coupled ...

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...

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 ...

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

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 ...

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 ...

One of the objectives of Pharmacometry (PMX) population modeling is the identification of significant and clinically relevant relationships between parameters and covariates. Here, we demonstrate how this complex selection task could benefit from supervise ...

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

In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory ...

To solve hyperbolic conservation laws on general grids we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite dierence method (RBF-TeCNOp) and an entropy s ...

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we ...

Parallel-in-time integration is an often advocated approach for extracting parallelism in the solution of PDEs beyond what is possible using spacial domain decomposition tech- niques. Due to the comparatively low parallel efficiency of parallel-in-time int ...

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 ...

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

Jan Sickmann Hesthaven

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Reduced basis methods for numerical room acoustic simulations with parametrized boundaries

Efficient Absorbing Layers for Weakly Compressible Flows

Projective multiscale time-integration for electrostatic particle-in-cell methods

Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

Structure preserving model reduction of parametric Hamiltonian systems

Population pharmacokinetic model selection assisted by machine learning

Monitoring of water table level and volume of water in a porous storage by seismic data

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

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

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

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

Adaptive WENO methods based on radial basis functions reconstruction

Fast screening of covariates in population models empowered by machine learning

A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

Reduced basis multiscale finite element methods for elliptic problems

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

Fault Tolerance in the Parareal Method

Structure-Preserving Reduced Basis Methods For Poisson Systems

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems