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Advances in applied mathematics and Mechanics 2021年第1期13卷 119-139页

作者： Mohamed Kara Salim Mesbahi Philippe Angot Applied Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Fundamental and Numerical Mathematics Laboratory Department of MathematicsFaculty of SciencesFerhat Abbas UniversitySetifAlgeria Aix-Marseille Universit´e Institut de Math´ematiques de MarseilleCNRS UMR 7373MarseilleFrance

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume *** main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious ***,we present a cell-centered finite volume method to discretize the fictitious domain *** proposed method is numerically validated for different test *** work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

关键词： Fictitious domain method sharp interface elasticity system jump embedded boundary conditions finite volume method

Consistent and Asymptotic-Preserving Finite-Volume Robin Transmission Conditions for Singularly Perturbed Elliptic Equations 26th

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Consistent and Asymptotic-Preserving Finite-Volume Robin Tra...

26th International Conference on Domain Decomposition Methods, 2020

作者： Gander, Martin J. Lunowa, Stephan B. Rohde, Christian Section de Mathématiques Université de Genève Rue du Conseil-Général 7-9 Genève SuisseCP 64 1205 Switzerland Computational Mathematics UHasselt – Hasselt University Agoralaan D 3590 Diepenbeek Hasselt Belgium Institute for Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany

ISBN: (纸本)9783030950248

Adaptive Dirichlet–Neumann and Robin–Neumann algorithms for singularlyperturbed advection-diffusion equations were introduced in [2], accounting for transport along characteristics, see also [6] for the discrete setting and damped versions using a modified quadrature rule to recover the hyperbolic limit. Non-overlapping Schwarz DDMs with Robin transmission conditions (TCs) applied to advectiondiffusion equations were analyzed in [1, 10] and a stabilized finite-element method for singularly perturbed problems was discussed in [9], see also [3, 4] and references therein for heterogeneous couplings. However, the behavior of these DDMs in the limit of vanishing diffusion has not been addressed. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Advection

A MULTIPOINT PERTURBATION FORMULA FOR EIGENVALUE PROBLEMS

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arXiv 2023年

作者： Dusson, Geneviève Garrigue, Louis Stamm, Benjamin Laboratoire de Mathématiques de Besançon UMR CNRS 6623 Université de Franche-Comté 16 route de Gray Besançon25030 France Laboratoire "analyse géométrie modélisation" CY Cergy Paris Université Cergy-Pontoise95302 France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart70569 Germany

Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of a Hamiltonian where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby Hamiltonians are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory. © 2023, CC BY.

关键词： Hamiltonians

A volume-averaging and stochastic turbulence modeling framework for homogeneous roughness-induced drag in turbulent flows

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PAMM 2024年第3期24卷

作者： Juan A. Medina Méndez Adrián Parra Lafuente Heiko Schmidt Numerical Fluid and Gas Dynamics BTU Cottbus-Senftenberg Cottbus Germany Industrial Mathematics Department of Applied Math for Aerospace Engineering Universidad Politécnica de Madrid Madrid Spain

The goal of this work is the formulation of a model for the parameterization of homogeneous roughness-induced drag in turbulent flow simulations. We characterize rough surfaces using their surface-area moments of roughness-peaks. Additionally, we consider a probabilistic self-similar power law distribution for the roughness heights, in such a way that an assumed set of discrete roughness elements can behave as a probabilistic fractal set. Upon these assumptions, the surface characterization is complete and yields wall-normal profiles of porosity, average roughness element diameter, and equivalent pore diameter of the roughness affected porous flow. The profiles are supplied to a (pore-based) Reynolds number and porosity-based drag parameterization for staggered cylinder arrays available in the literature, as well as a one-dimensional map-based turbulence model, the one-dimensional turbulence (ODT) model. The purpose of the latter is a way to provide the missing effects of the equivalent dispersion tensor in the porous flow close to the rough surface, as well as that of the nonlinear turbulent transport away from the wall. Simulations are then carried out in order to evaluate the effects of two different rough surfaces on a turbulent channel flow, comparing results with existing direct numerical simulation (DNS) data. Overall, reasonable agreement is obtained, which suggests that, by using the proposed model, it is possible to model the effects of rough surfaces on wall-bounded turbulent flows, without the explicit need of the full topological representation of the surface on the numerical domain. To that extent, one clear flow control application for the suggested approach would be that of drag-based surface optimization.

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A Quasi Time-Reversible scheme based on density matrix extrapolation on the Grassmann manifold for Born-Oppenheimer Molecular Dynamics

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arXiv 2023年

作者： Pes, Federica Polack, Étienne Mazzeo, Patrizia Dusson, Geneviève Stamm, Benjamin Lipparini, Filippo Dipartimento di Chimica e Chimica Industriale Università di Pisa Via G. Moruzzi 13 Pisa56124 Italy CERMICS École des Ponts and Inria Paris 6 & 8 avenue Blaise Pascal Marne-la-Vallé 77455 France Laboratoire de Mathématiques de Besançon UMR CNRS 6623 Université de Franche-Comté 16 route de Gray Besançon25030 France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart70569 Germany

This article proposes a so-called Quasi Time-Reversible (QTR G-Ext) scheme based on Grassmann extrapolation of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics simulations. The method shows excellent results on four large molecular systems, ranging from 21 to 94 atoms simulated with Kohn-Sham density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations, while keeping a similar energy drift as in the extended Lagrangian Born-Oppenheimer method. © 2023, CC BY-NC-SA.

关键词： Extrapolation

A finite-volume tracking scheme for two-phase compressible flow 16th

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16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

作者： Chalons, Christophe Magiera, Jim Rohde, Christian Wiebe, Maria Laboratoire de Mathématiques de Versailles UVSQ CNRS Université Paris-Saclay Versailles78035 France Institute for Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany

ISBN: (纸本)9783319915449

We propose a finite-volume tracking method in multiple space dimensions to approximate weak solutions of the hydromechanical equations that allow two-phase behavior. The method relies on a moving mesh ansatz such that the phase boundary is represented as a sharp interface without any artificial smearing. At the interface, an approximate solver is applied, such that the exact Riemann solution is not required. From precedent work, it is known that the method is locally conservative and recovers planar traveling wave solutions exactly. To demonstrate the efficiency and reliability of the new scheme, we test it on various situations for liquid–vapor flow. © Springer International Publishing AG, part of Springer Nature 2018.

关键词： Two phase flow

Simultaneous elastic shape optimization for a domain splitting in bone tissue engineering

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arXiv 2018年

作者： Dondl, Patrick Poh, Patrina S.P. Rumpf, Martin Simon, Stefan Institute for Applied Math University of Freiburg Germany Julius Wolff Institute Charité - Universitätsmedizin Berlin Germany Institute for Numerical Simulation University of Bonn Germany

This paper deals with the simulateneous optimization of a subset O0 of some domain Ω and its complement O1 = Ω \ O0 both considered as separate elastic objects subject to a set of loading scenarios. If one asks for a configuration which minimizes the maximal elastic cost functional both phases compete for space since elastic shapes usually get mechanically more stable when being enlarged. Such a problem arises in biomechanics where a bioresorbable polymer scaffold is implanted in place of lost bone tissue and in a regeneration phase new bone tissue grows in the scaffold complement via osteogenesis. In fact, the polymer scaffold should be mechanically stable to bear loading in the early stage regeneration phase and at the same time the new bone tissue grown in the complement of this scaffold should as well bear the loading. Here, this optimal subdomain splitting problem with appropriate elastic cost functionals is introduced and existence of optimal two phase configurations is established for a regularized formulation. Furthermore, based on a phase field approximation a finite element discretization is derived. numerical experiments are presented for the design of optimal periodic scaffold microstructure.65K10, 49M30, 74B05, 35Q92 Copyright © 2018, The Authors. All rights reserved.

关键词： Shape optimization

Parseval Proximal Neural Networks

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arXiv 2019年

作者： Hasannasab, Marzieh Hertrich, Johannes Neumayer, Sebastian Plonka, Gerlind Setzer, Simon Steidl, Gabriele 1Department of Mathematics Technische Universität Kaiserslautern Paul-Ehrlich-Str. 31 D-67663 Kaiserslautern Germany {name}@mathematik.uni-kl.de. 2Institute for Numerical and Applied Mathematics Göttingen University Lotzestr. 16-18 37083 Göttingen Germany {name}@math.uni-goettingen.de. 3 simon.setzer@***.

The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert space. Second, we use our findings to establish so-called proximal neural networks (PNNs) and stable Parseval (frame) proximal neural networks (PPNNs). Let H and K be real Hilbert spaces, b ∈ K and T ∈ B(H, K) a linear operator with closed range and Moore-Penrose inverse T†. Based on the well-known characterization of proximity operators by Moreau, we prove that for any proximity operator Prox: K → K the operator T† Prox(T · +b) is a proximity operator on H equipped with a suitable norm. In particular, it follows for the frequently applied soft shrinkage operator Prox = Sλ: l2 → l2 and any frame analysis operator T : H → l2, that the frame shrinkage operator T† Sλ T is a proximity operator in a suitable Hilbert space. Further, the concatenation of proximity operators on Rd equipped with different norms establishes a PNN. If the network arises from Parseval frame analysis or synthesis operators, it forms an averaged operator, called PPNN. The involved linear operators, respectively their transposed operators, are in a Stiefel manifold, so that minimization methods on Stiefel manifolds can be applied for training such networks. Finally, some proof-of-the concept examples demonstrate the performance of PPNNs. Copyright © 2019, The Authors. All rights reserved.

关键词： Hilbert spaces

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

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arXiv 2020年

作者： Berre, Inga Boon, Wietse M. Flemisch, Bernd Fumagalli, Alessio Gläser, Dennis Keilegavlen, Eirik Scotti, Anna Stefansson, Ivar Tatomir, Alexandru Brenner, Konstantin Burbulla, Samuel Devloo, Philippe Duran, Omar Favino, Marco Hennicker, Julian Lee, I-Hsien Lipnikov, Konstantin Masson, Roland Mosthaf, Klaus Chiara Nestola, Maria Giuseppina Ni, Chuen-Fa Nikitin, Kirill Schädle, Philipp Svyatskiy, Daniil Yanbarisov, Ruslan Zulianp, Patrick Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm11428 Sweden Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Pfaffenwaldring 61 Stuttgart70569 Germany Laboratory for Modeling and Scientific Computing MOX Politecnico di Milano p.za Leonardo da Vinci 32 Milano20133 Italy Department of Applied Geology Geosciences Center University of Göttingen Goldschmidtstrasse 3 Göttingen37077 Germany Department of Earth Sciences Uppsala University Villavägen 16 UppsalaS-75236 Sweden University of Côte d’Azur CNRS INRIA LJAD Nice France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany FEC Universidade Estadual de Campinas Cidade Universitária R. Josiah Willard Gibbs 85 Campinas-SPCEP 13083-839 Brazil Institute of Earth Sciences University of Lausanne Building Geopolis UNIL-Mouline Lausanne1015 Switzerland Section de Mathématiques Université de Genève 2-4 rue du Lièvre CP 64 Genève1211 Switzerland Graduate Institute of Applied Geology National Central University Taiwan Center for Environmental Studies National Central University Taiwan Los Alamos National Laboratory New Mexico United States Department of Environmental Engineering Technical University of Denmark Bygningstorvet Building 115 Kgs. Lyngby2800 Denmark Numerical Simulation in Science Medicine and Engineering Group Institute of Computational Science Università della Svizzera italiana. Via G. Buffi 13 Lugano Ticino6900 Switzerland Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences Moscow Russia ETH Zürich Geothermal Energy and Geofluids Group Institute of Geophysics Zürich8092 Switzerland

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases. Copyright © 2020, The Authors. All rights reserved.

关键词： numerical methods

QTT-isogeometric solver in two dimensions

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arXiv 2018年

作者： Markeeva, L. Tsybulin, I. Oseledets, I. Center for Computational and Data-Intensive Science and Engineering Skolkovo Institute of Science and Technology Moscow Russia Department of Applied Math and Control Moscow Institute of Physics and Technology Moscow Russia Laboratory of Fluid Dynamics and Seismics Moscow Institute of Physics and Technology Moscow Russia Institute of Numerical Mathematics Russian Academy of Sciences Moscow Russia