Jan Sickmann Hesthaven

Prof. Hesthaven received an M.Sc. in computational physics from the Technical University of Denmark (DTU) in August 1991. During the studies, the last 6 months of 1989 was spend at JET, the european fusion laboratory in Culham, UK. Following graduation, he was awarded a 3 year fellowship to begin work towards a Ph.D. at Riso National Laboratory in the Department of Optics and Fluid Dynamics. During the 3 years of study, the academic year of 1993-1994 was spend in the Division of Applied Mathematics at Brown University and three 3 months during the summer of 1994 in Department of Mathematics and Statistics at University of New Mexico. In August 1995, he recieved a Ph.D. in Numerical Analysis from the Institute of Mathematical Modelling (DTU). Following graduation in August 1995, he was awarded an NSF Postdoctoral Fellowship in Advanced Scientific Computing and was approinted Visiting Assistant Professor in the Division of Applied Mathematics at Brown University. In December of 1996, he was appointed consultant to the Institute of Computer Applications in Science and Engineering(ICASE) at NASA Langley Research Center (NASA LaRC). As of July 1999, he was appointed Assistant Professor of Applied Mathematics, in September 2000 he was awarded an Alfred P. Sloan Fellowship, as of July 2001 he was awarded a Manning Assistant Professorship, and in March 2002, he was awarded an NSF Career Award. In January 2003, he was promoted to Associate Professor of Applied Mathematics with tenure and in May 2004 he was awarded Philip J. Bray Award for Excellence in Teaching in the Sciences (the highest award given for teaching excellence in all sciences at Brown University). He was promoted to Professor of Applied Mathematics as of July 2005. From October 2006 to June 2013, he was the Founding Director of the Center for Computation and Visualization (CCV) at Brown University. As of October 2007, he holds the (honorary) title of Professor (Adjunct) at the Technical University of Denmark. In November 2009, he successfully defended his dr.techn thesis at the Technical University of Denmark and was rewarded the degree of Doctor Technices -- the highest academic distinction awarded based on ... substantial and lasting contributions that has helped to move the research area forward and penetrated into applications. As grant Co-PI he served from Aug 2010 to June 2013 as Deputy Director of the Institute of Computational and Experimental Research in Mathematics (ICERM), the newest NSF Mathematical Sciences Research Institute. After having spend his entire academic career at Brown University, Prof Hesthaven decided to pursue new challenges and joined the Mathematics Institute of Computational Science and Engineering (MATHICSE) at Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland in July 2013. In March 2014 he was elected SIAM Fellow for contributions to high-order methods for partial differential equations.

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Analyse numérique

L’analyse numérique est une discipline à l'interface des mathématiques et de l'informatique. Elle s’intéresse tant aux fondements qu’à la mise en pratique des méthodes permettant de résoudre, par des

Méthode des éléments finis

En analyse numérique, la méthode des éléments finis (MEF, ou FEM pour finite element method en anglais) est utilisée pour résoudre numériquement des équations aux dérivées partielles. Celles-ci pe

Neural network

A neural network can refer to a neural circuit of biological neurons (sometimes also called a biological neural network), a network of artificial neurons or nodes in the case of an artificial neur

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

Niccolo' Discacciati, Jan Sickmann Hesthaven

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 problems with parametrized interface boundary conditions, while we combine them using domain decomposition techniques during the online phase. We show the potential of the proposed approach in terms of accuracy, computational performance and robustness in a series of test cases, including nonlinear and multi-physics problems.

WILEY2023

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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 for shock-dominated flows. Furthermore, for Euler systems, ROMs built on the conservative and the skew-symmetric forms of the governing equation are compared. To ensure efficiency, the discrete empirical interpolation method (DEIM) is employed. An alternative reduction approach, exploring the sparsity of viscosity is also investigated for the viscous terms. A number of one- and two-dimensional benchmark cases are considered to test the performance of the proposed models. Results show that stable computations for shock-dominated cases can be achieved with ROMs built on both the conservative and the skew-symmetric forms without additional stabilization components other than the viscosity model and filtering. Under the same parameters, the skew-symmetric form shows better robustness and accuracy than its conservative counterpart, while the conservative form is superior in terms of efficiency.

GLOBAL SCIENCE PRESS2022

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Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Jan Sickmann Hesthaven

Projection-based reduced order models (ROM) based on the weak form and the strong form of the discontinuous Galerkin (DG) method are proposed and compared for shock-dominated problems. The incorporation of dissipation components of DG in a consistent manner, including the upwinding flux and the localized artificial viscosity model, is employed to enhance stability of the ROM. To ensure efficiency, the discrete empirical interpolation method (DEIM) is adopted to enable hyper-reduction, for which the upwinding flux is decomposed into the central part and the dissipation part. The maximum local wave speed in the upwinding dissipation part is compressed and approximated using the DEIM approach, and the same strategy is applied to the artificial viscosity. Energy stability is proved with the strong-form-based ROM prior to hyper-reduction for the one-dimensional scalar cases. Eigenvalue spectrum is analyzed to verify and compare the stability properties of the two proposed ROMs. Several benchmark cases are conducted to test the performance of the proposed models. Results show that stable computations with reasonable acceleration for shock-dominated cases can be achieved with the ROM built on the strong form. (C) 2022 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

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