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Jan Sickmann Hesthaven

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Publications associées (102)

Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

Jan Sickmann Hesthaven, Reza Mokhtari

This paper is devoted to determining a space-dependent source term in an inverse problem of the time-fractional diffusion equation. We use a fully-discrete method based on a finite difference scheme in time and a local discontinuous Galerkin method (LDG) i ...

Springer2017

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

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

Jan Sickmann Hesthaven, Paolo Gatto

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 ...

Springer Verlag2017

Efficient Absorbing Layers for Weakly Compressible Flows

Jan Sickmann Hesthaven, Zhen Gao

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 ...

2016

On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations

Jan Sickmann Hesthaven

We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional para ...

Springer Verlag2016

Spectral methods for tempered fractional differential equations

Jan Sickmann Hesthaven, Lijing Zhao

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouvi ...

2016

Fault Tolerance in the Parareal Method

Jan Sickmann Hesthaven, Allan Svejstrup Nielsen

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 ...

Assoc Computing Machinery2016

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

Jan Sickmann Hesthaven, Paolo Gatto

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 ...

Springer Verlag2015

Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics

Jan Sickmann Hesthaven

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 ...

Springer2015

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

Reduced basis multiscale finite element methods for elliptic problems

Jan Sickmann Hesthaven

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 ...

Society for Industrial and Applied Mathematics2015

Hyperbolic Problems: Theory and Computation

Jan Sickmann Hesthaven

Springer Verlag2015

An Adjoint Approach for Stabilizing the Parareal Method

Yvon Maday, Jan Sickmann Hesthaven, Allan Svejstrup Nielsen

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 ...

2015

A Multi-domain Spectral Method for Time-fractional Differential Equations

Jan Sickmann Hesthaven

This paper proposes an approach for high-order time integration within a multi-domain setting for time- fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to p ...

Elsevier2015

Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"

Jan Sickmann Hesthaven

Academic Press Inc Elsevier Science2015

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

Jan Sickmann Hesthaven

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 ...

Elsevier2014

Applications of Model Reduction Techniques in Aerospace Combustors

Jan Sickmann Hesthaven

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 ...

2014

High-order multiscale finite element method for elliptic problems

Jan Sickmann Hesthaven

In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite ...

Society for Industrial and Applied Mathematics2014

Fast prediction and evaluation of gravitational waveforms using surrogate models

Jan Sickmann Hesthaven

We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the generation of waveforms us ...

American Physical Society2014

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

Benjamin Stamm, Jan Sickmann Hesthaven

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

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