检索结果-内蒙古大学图书馆

Parallel block-preconditioned monolithic solvers for fluid-structure-interaction problems

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Jodlbauer, D. Langer, U. Wick, T. Doctoral Program on Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria Institut für Angewandte Mathematik Leibniz Universität Hannover Welfengarten 1 Hannover30167 Germany

In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large, ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom, and, in addition, exhibit superlinear grow in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block LDU-factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two- and three-dimensional test cases permitting large deformations.65N30, 65M60, 49M15, 35Q74 Copyright © 2018, The Authors. All rights reserved.

关键词： Iterative methods

The Athena++ adaptive mesh refinement framework: Design and magnetohydrodynamic solvers

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Earth and Space Science Osaka University Toyonaka Osaka560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93107 United States School of Natural Sciences Institute for Advanced Study PrincetonNJ08544 United States Astronomical Institute Tohoku University Sendai Miyagi980-8578 Japan Argonne National Laboratory LemontIL60439 United States

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

Phase retrieval with holography and untrained priors: Tackling the challenges of low-photon nanoscale imaging

学校读者我要写书评

暂无评论

arXiv 2020年

作者： Lawrence, Hannah Barmherzig, David A. Li, Henry Eickenberg, Michael Gabrié, Marylou Massachusetts Institute of Technology CambridgeMA United States Center for Computational Mathematics Flatiron Institute New YorkNY United States Program in Applied Mathematics Yale University Connecticut United States Center for Data Science New York University New YorkNY United States

Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography, includes a reference object that is placed adjacent to the specimen of interest before measurements are collected. The resulting inverse problem, known as holographic phase retrieval, is well-known to have improved problem conditioning relative to the original. This innovation, i.e. Holographic CDI, becomes crucial at the nanoscale, where imaging specimens such as viruses, proteins, and crystals require low-photon measurements. This data is highly corrupted by Poisson shot noise, and often lacks low-frequency content as well. In this work, we introduce a dataset-free deep learning framework for holographic phase retrieval adapted to these challenges. The key ingredients of our approach are the explicit and flexible incorporation of the physical forward model into an automatic differentiation procedure, the Poisson log-likelihood objective function, and an optional untrained deep image prior. We perform extensive evaluation under realistic conditions. Compared to competing classical methods, our method recovers signal from higher noise levels and is more resilient to suboptimal reference design, as well as to large missing regions of low frequencies in the observations. Finally, we show that these properties carry over to experimental data acquired on optical wavelengths. To the best of our knowledge, this is the first work to consider a dataset-free machine learning approach for holographic phase retrieval. Copyright © 2020, The Authors. All rights reserved.

关键词： Holography

Accelerating GMRES with deep learning in real-time

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Luna, Kevin Klymko, Katherine Blaschke, Johannes P. Program in Applied Mathematics The University of Arizona United States Computational Research Division Lawrence Berkeley National Laboratory United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory United States

GMRES is a powerful numerical solver used to find solutions to extremely large systems of linear equations. These systems of equations appear in many applications in science and engineering. Here we demonstrate a real-time machine learning algorithm that can be used to accelerate the time-to-solution for GMRES. Our framework is novel in that is integrates the deep learning algorithm in an in situ fashion: the AI-accelerator gradually learns how to optimizes the time to solution without requiring user input (such as a pre-trained data set). We describe how our algorithm collects data and optimizes GMRES. We demonstrate our algorithm by implementing an accelerated (MLGMRES) solver in Python. We then use MLGMRES to accelerate a solver for the Poisson equation - a class of linear problems that appears in may applications. Informed by the properties of formal solutions to the Poisson equation, we test the performance of different neural networks. Our key takeaway is that networks which are capable of learning non-local relationships perform well, without needing to be scaled with the input problem size, making them good candidates for the extremely large problems encountered in high-performance computing. For the inputs studied, our method provides a roughly 2× acceleration. Copyright © 2021, The Authors. All rights reserved.

关键词： Poisson equation

Multilevel Particle Filters for Partially Observed McKean-Vlasov Stochastic Differential Equations

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

Limited angle acousto-electrical tomography

学校读者我要写书评

暂无评论

arXiv 2017年

作者： Hubmer, Simon Knudsen, Kim Li, Changyou Sherina, Ekaterina Johannes Kepler University Linz Doctoral Program Computational Mathematics Altenbergerstraße 69 LinzA-4040 Austria Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark School of Electronics and Information Northwestern Polytechnical University Xian China Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.65J22, 35R30, 65M32 Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary conditions

Constraining the interaction between dark sectors with future HI intensity mapping observations

学校读者我要写书评

暂无评论

Physical Review D 2018年第8期97卷 083504-083504页

作者： Xiaodong Xu Yin-Zhe Ma Amanda Weltman Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch 7701 Cape Town South Africa School of Chemistry and Physics University of KwaZulu-Natal Durban 4000 South Africa NAOC-UKZN Computational Astrophysics Centre (NUCAC) University of KwaZulu-Natal Durban 4000 South Africa School of Natural Sciences Institute for Advanced Study Olden Lane Princeton New Jersey 08540 USA

We study a model of interacting dark matter and dark energy, in which the two components are coupled. We calculate the predictions for the 21-cm intensity mapping power spectra, and forecast the detectability with future single-dish intensity mapping surveys (BINGO, FAST and SKA-I). Since dark energy is turned on at z∼1, which falls into the sensitivity range of these radio surveys, the HI intensity mapping technique is an efficient tool to constrain the interaction. By comparing with current constraints on dark sector interactions, we find that future radio surveys will produce tight and reliable constraints on the coupling parameters.

关键词： Cosmological parameters Dark energy Dark matter Radio, microwave, & sub-mm astronomy

HIGH-PERFORMANCE FINITE ELEMENTS WITH MFEM

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Andrej, Julian Atallah, Nabil Bäcker, Jan-Phillip Camier, John Copeland, Dylan Dobrev, Veselin Dudouit, Yohann Duswald, Tobias Keith, Brendan Kim, Dohyun Kolev, Tzanio Lazarov, Boyan Mittal, Ketan Pazner, Will Petrides, Socratis Shiraiwa, Syunichi Stowell, Mark Tomov, Vladimir Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA United States TU Dortmund University Dortmund Germany CERN and Technical University of Munich Munich Germany Division of Applied Mathematics Brown University ProvidenceRI United States Computational Engineering Division Lawrence Livermore National Laboratory LivermoreCA United States Fariborz Maseeh Department of Mathematics and Statistics Portland State University PortlandOR United States Princeton Plasma Physics Laboratory PrincetonNJ United States

The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational physics and engineering applications across a number of domains. This paper describes some of the recent research and development in MFEM, focusing on performance portability across leadership-class supercomputing facilities, including exascale supercomputers, as well as new capabilities and functionality, enabling a wider range of applications. Much of this work was undertaken as part of the Department of Energy’s Exascale Computing Project (ECP) in collaboration with the Center for Efficient Exascale Discretizations (CEED). Copyright © 2024, The Authors. All rights reserved.

关键词： Finite element method

iMapD: Intrinsic map dynamics exploration for uncharted effective free energy landscapes

学校读者我要写书评

暂无评论

arXiv 2016年

作者： Chiavazzo, Eliodoro Coifman, Ronald R. Covino, Roberto William Gear, C. Georgiou, Anastasia S. Hummer, Gerhard Kevrekidis, Ioannis G. Energy Department Politecnico di Torino Torino10129 Italy Department of Mathematics Program in Applied Mathematics Yale University New HavenCT06510 United States Max Planck Institute of Biophysics Frankfurt am Main60438 Germany Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Institute of Biophysics Goethe University Frankfurt am Main60438 Germany PACM Princeton University PrincetonNJ08544 United States IAS-TUM Garching Germany

We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extraction of coarse-grained, macroscopic information from atomistic or stochastic (here Molecular Dynamics, MD) simulations. The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator towards new, unexplored phase space regions by exploiting the smoothness of the (gradually, as the exploration progresses) revealed intrinsic low-dimensional geometry of the FES. Copyright © 2016, The Authors. All rights reserved.

关键词： Free energy