Jan Sickmann Hesthaven

Related publications (256)

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Related publications (256)

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism

Qian Wang, Jan Sickmann Hesthaven, Nicolò Ripamonti

Closure modeling based on the Mori-Zwanzig formalism has proven effective to improve the stability and accuracy of projection-based model order reduction. However, closure models are often expensive and infeasible for complex nonlinear systems. Towards eff ...

2020

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

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

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Rare event simulation for large-scale structures with local nonlinearities

Jan Sickmann Hesthaven, Zhenying Zhang

ELSEVIER SCIENCE SA2020

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 ...

2020

Hybrid high-resolution RBF-ENO method

Jan Sickmann Hesthaven, Fabian Mönkeberg

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. The RBF-ENO method is highly flexible in terms of geometry, but its stenci ...

2020

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

Jan Sickmann Hesthaven, Reza Mokhtari

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

An edge detector based on artificial neural network with application to hybrid Compact-WENO finite difference schemes

Jan Sickmann Hesthaven, Zhen Gao

A new approach is proposed to detect edges based on an artificial neural network (ANN). Some elementary continuous and discontinuous functions interpolated in the polynomial space and their continuity are used as the training sets to train a back propagati ...

Springer/Plenum2020

Effective diffusion tensor measured by diffusion MRI of moving and deforming domains

Jan Sickmann Hesthaven

The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torre ...

2020

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Two-Dimensional RBF-ENO Method on Unstructured Grids

Jan Sickmann Hesthaven, Fabian Mönkeberg

SPRINGER/PLENUM PUBLISHERS2020

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism

Qian Wang, Jan Sickmann Hesthaven, Nicolò Ripamonti

2020

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven

Boris Bonev