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arXiv 2017年

作者： Egger, Herbert Pietschmann, Jan-Frederik Schlottbom, Matthias Ag Numerical Analysis and Scientific Computing Department of Mathematics Tu Darmstadt Dolivostr. 15 Darmstadt64293 Munster Einsteinstr. 62 MunsterD 48149 Department of Applied Mathematics University of Twente P.O. Box 217 AE Enschede7500

We consider the identification of nonlinear diffusion coeficients of the form a(t;u) or a(u) in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using partial knowledge of the Dirichlet-To-Neumann map. The proof of our main result relies on the construction of a series of appropriate Dirichlet data and test functions with a particular singular behavior at the boundary. This allows us to localize the analysis and to separate the principal part of the equation from the remaining terms. We therefore do not require specific knowledge of lower order terms or initial data which allows to apply our results to a variety of applications. This is illustrated by discussing some typical examples in detail. Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

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AFast Solver for an H_(1) Regularized PDE-Constrained Optimization Problem

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Communications in Computational Physics 2016年第1期19卷 143-167页

作者： Andrew T.Barker Tyrone Rees Martin Stoll Center for Applied Scientific Computing Lawrence Livermore National LaboratoryMail Stop L-561LivermoreCA 94551USA Numerical Analysis Group Scientific Computing DepartmentRutherford Appleton LaboratoryChiltonDidcotOxfordshireOX110QXUnited Kingdom Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical SystemsSandtorstr.139106MagdeburgGermany

In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle *** propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

关键词： Preconditioning Krylov methods PDE-constrained optimization optimal control of PDEs

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A STUDY of multigrid smoothers used in compressible CFD based on the convection diffusion equation 7

A STUDY of multigrid smoothers used in compressible CFD base...

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7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016

作者： Birken, Philipp Bull, Jonathan Jameson, Antony Lund University Centre for the Mathematical Sciences Numerical Analysis Box 118 Lund22100 Sweden Uppsala University Division of Scientific Computing Dept. of Information Technology Box 337 Uppsala75105 Sweden Stanford University Department of Aeronautics and Astronautics StanfordCA94305 United States

ISBN: (纸本)9786188284401

We look at multigrid methods for unsteady viscous compressible flows. We specifically target smoothers that can be used in parallel and without computation of a Jacobian, which are particlarly attractive candidates in the context of Discontinuous Galerkin discretizations. In CFD, a plethora of nonlinear smoothers have been suggested which are hard to analyze. Our methodology is to use a linear model problem, here the convection diffusion equation, to be able to classify and compare smoothers better. Specifically, we consider explicit and implicit pseudo time iterations, GMRES as a smoother, SGS and implicit line smoothers. We relate GMRES to explicit Runge-Kutta smoothers, identify implicit line smoothers as Block Jacobi and analyze the potential of implicit pseudo time iterations. Finally, we discuss the relation between methods for steady and unsteady flows. numerical results show that GMRES is a very attractive smoother in this context.

关键词： Unsteady flow

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A note on terminology in multigrid methods

A note on terminology in multigrid methods

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Joint 87th Annual Meeting on the International Association of Applied Mathematics and Mechanics, GAMM 2016 and Deutsche Mathematiker‐Vereinigung, DMV 2016

We compare terminology used in the literature on multigrid methods for compressible computational fluid dynamics to that used in linear multigrid theory. Several popular iterative and direct smoothers are presented side-by-side using the same terminology. We argue for greater analysis of these methods in order to place them into a more rigorous framework and to identify the most promising candidates for future development. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： Terminology

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Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE

Advances concerning multiscale methods and uncertainty quant...

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International Conference on Software for Exascale computing, SPPEXA 2015

作者： Bastian, Peter Engwer, Christian Fahlke, Jorrit Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Milk, René Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Heidelberg Germany Institute for Computational and Applied Mathematics University of Münster Münster Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Institute for Applied Mathematics TU Dortmund Dortmund Germany Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany Institut für Mathematik TU Clausthal-Zellerfeld Clausthal-Zellerfeld Germany

ISBN: (纸本)9783319405261

In this contribution we present advances concerning efficient parallel multiscale methods and uncertainty quantification that have been obtained in the frame of the DFG priority program 1648 Software for Exascale computing (SPPEXA) within the funded project EXA-DUNE. This project aims at the development of flexible but nevertheless hardware-specific software components and scalable high-level algorithms for the solution of partial differential equations based on the DUNE platform. While the development of hardware-based concepts and software components is detailed in the companion paper (Bastian et al., Hardware-based efficiency advances in the EXA-DUNE project. In: Proceedings of the SPPEXA Symposium 2016, Munich, 25–27 Jan 2016), we focus here on the development of scalable multiscale methods in the context of uncertainty. © Springer International Publishing Switzerland 2016.

关键词： Uncertainty analysis

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Hardware-Based efficiency advances in the EXA-DUNE project

Hardware-Based efficiency advances in the EXA-DUNE project

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International Conference on Software for Exascale computing, SPPEXA 2015

作者： Bastian, Peter Engwer, Christian Fahlke, Jorrit Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Milk, René Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Heidelberg Germany Institute for Computational and Applied Mathematics University of Münster Münster Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Institute of Applied Mathematics TU Dortmund Dortmund Germany Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany Institut für Mathematik TU Clausthal-Zellerfeld Clausthal-Zellerfeld Germany

ISBN: (纸本)9783319405261

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the EXA-DUNE project, part of the DFG priority program 1648 Software for Exascale computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the provenMPI-level scalability of the framework. The higher-level aspects of the EXADUNE project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE. In: Proceedings of the SPPEXA Symposium, 2016). © Springer International Publishing Switzerland 2016.

关键词： Uncertainty analysis

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INTRODUCTION

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Bulletin of the American Meteorological Society 2024年第8期105卷 S1-S11页

作者： Boyer, T. Blunden, J. Dunn, R.J.H. NOAA/NESDIS National Centers for Environmental Information Silver Spring Maryland NOAA/NESDIS National Centers for Environmental Information Asheville North Carolina Met Office Hadley Centre Exeter United Kingdom European Centre for Medium-Range Weather Forecasts Reading United Kingdom University of Maryland College Park Maryland Scripps Institution of Oceanography University of California San Diego La Jolla California NOAA/NWS National Centers for Environmental Prediction Climate Prediction Center College Park Maryland Brandenburg University of Technology (BTU) Cottbus-Senftenberg Germany Servicio Meteorológico Nacional Buenos Aires Argentina NOAA/OAR Physical Sciences Laboratory Boulder Colorado European Centre for Medium-Range Weather Forecasts Bonn Germany Center for Geophysical Research and School of Physics University of Costa Rica San José Costa Rica Department of Meteorology and National Centre for Earth Observation University of Reading Reading United Kingdom Centro Nacional de Monitoramento e Alertas de Desastres Naturais CEMADEN São Paulo Brazil Université Grenoble Alpes Institut des Géosciences de l’Environnement IRD CNRS Grenoble INP Grenoble France Hampton University Hampton Virginia Seychelles Meteorological Authority Mahe Seychelles Section for Glaciers Ice and Snow Norwegian Water Resources and Energy Directorate Oslo Norway National Research Institute for Agriculture Food and Environment (INRAE) CARRTEL Université Savoie Mont Blanc Thonon les Bains France Graduate School of Agriculture Osaka Metropolitan University Sakai Japan Science Faculty Universidad Nacional de Colombia Bogotá Colombia University of Bremen Bremen Germany NOAA Global Monitoring Laboratory Boulder Colorado Servicio Nacional de Meteorología e Hidrología del Perú Lima Perú Centro de Investigaciones sobre Desertificación – Spanish National Research Council (CSIC-UV-GVA) Valencia Spain Hydro-Climate Extremes Lab (H-CEL) Ghent University Ghent Belgium Department o

In 2023, La Niña conditions that generally prevailed in the eastern Pacific Ocean from mid-2020 into early 2023 gave way to a strong El Niño by October. Atmospheric concentrations of Earth’s major greenhouse gases—carbon dioxide, methane, and nitrous oxide—all increased to record-high levels. The annual global average carbon dioxide concentration in the atmosphere rose to 419.3±0.1 ppm, which is 50% greater than the pre-industrial level. The growth from 2022 to 2023 was 2.8 ppm, the fourth highest in the record since the 1960s. The combined short-term effects of El Niño and the long-term effects of increasing levels of heat-trapping gases in the atmosphere contributed to new records for many essential climate variables reported here. The annual global temperature across land and oceans was the highest in records dating as far back as 1850, with the last seven months (June–December) having each been record warm. Over land, the globally averaged temperature was also record high. Dozens of countries reported record or near-record warmth for the year, including China and continental Europe as a whole (warmest on record), India and Russia (second warmest), and Canada (third warmest). Intense and widespread heatwaves were reported around the world. In Vietnam, an all-time national maximum temperature record of 44.2°C was observed at Tuong Duong on 7 May, surpassing the previous record of 43.4°C at Huong Khe on 20 April 2019. In Brazil, the air temperature reached 44.8°C in Araçuaí in Minas Gerais on 20 November, potentially a new national record and 12.8°C above normal. The effect of rising temperatures was apparent in the cryosphere, where snow cover extent by June 2023 was the smallest in the 56-year record for North America and seventh smallest for the Northern Hemisphere overall. Heatwaves contributed to the greatest average mass balance loss for Alpine glaciers around the world since the start of the record in 1970. Due to rapid volume loss beginning in 2021, St. A

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A note on terminology in multigrid methods

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PAMM 2016年第1期16卷

作者： Philipp Birken Jonathan Bull Antony Jameson Lund University Centre for the Mathematical Sciences Numerical Analysis Box 118 22100 Lund Uppsala University Division of Scientific Computing Dept. of Information Technology Box 337 75105 Uppsala Stanford University Department of Aeronautics & Astronautics Stanford CA 94305

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Adjoint error estimation for stochastic collocation methods 1

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2nd Workshop on Sparse Grids and Applications, SGA 2012

作者： Schieche, Bettina Lang, Jens Numerical Analysis and Scientific Computing Department of Mathematics Technische Universität Darmstadt Dolivostr. 15 Darmstadt64293 Germany Numerical Analysis and Scientific Computing Department of Mathematics and Graduate School of Computational Engineering Technische Universität Darmstadt Dolivostr. 15 Darmstadt64293 Germany

ISBN: (数字)9783319045375

ISBN: (纸本)9783319045368

This paper deals with partial differential equations with random input data. An efficient way of solving such problems is adaptive stochastic collocation on sparse grids. For higher efficiency and a better understanding of the method, we derive adjoint error estimates for nonlinear stochastic solution functionals. The resulting adjoint problem also involves random parameters and can be treated by stochastic collocation as well. Only a few adjoint evaluations are required in order to estimate the deterministic error, while the stochastic error requires much more effort to be detected. To overcome these substantial additional costs, we suggest to replace the adjoint problem by a reduced model and demonstrate the applicability of the approach for nonlinear solution functionals and up to nine random dimensions. © Springer International Publishing Switzerland 2014.

关键词： Errors

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Uncertainty quantification for thermo-convective Poiseuille flow using stochastic collocation

Uncertainty quantification for thermo-convective Poiseuille ...

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作者： Schieche, Bettina Lang, Jens Graduate School of Computational Engineering Center of Smart Interfaces Numerical Analysis and Scientific Computing Department of Mathematics Dolivostrasse 15 64293 Darmstadt Germany

Simulations become more reliable if they include random effects. One way to express uncertainties in the describing parameters are correlated random fields. Typically, the resulting problem is a partial differential equation (PDE) with random parameters. These additional, stochastic dimensions can be discretised either by spectral methods or stochastic collocation. The aim of this work is to analyse effects of an uncertain heating condition for plane Poiseuille flow by means of an adaptive, anisotropic stochastic collocation method. Additionally, we are interested in how the heat exchange can be improved by small surface variations. We show that the fluctuations of the resulting flow continuously depend on the input fluctuations. Furthermore, we can find specific surface structures that improve the heat exchange. Copyright © 2014 Inderscience Enterprises Ltd.

关键词： Stochastic systems

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