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Communications on Applied mathematics and Computation 2020年第4期2卷 581-611页

作者： Hendrik Ranocha Katharina Ostaszewski Philip Heinisch Institute Computational Mathematics TU BraunschweigUniversitatsplatz 238106 BrunswickGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Institut für Angewandte Numerische Wissenschaft e.V.(IANW) Bienroder Straae 338110 BrunswickGermany Institut für Geophysik und Extraterrestrische Physik TU BraunschweigMendelssohnstraBe 338106 BrunswickGermany

In this article,discrete variants of several results from vector calculus are studied for clas-sical finite difference summation by parts operators in two and three space *** is shown that existence theorems for scalar/vector potentials of irrotational/solenoidal vector fields cannot hold discretely because of grid oscillations,which are characterised *** results in a non-vanishing remainder associated with grid oscillations in the discrete Helmholtz Hodge ***,iterative numerical methods based on an interpretation of the Helmholtz Hodge decomposition via orthogonal projections are pro-posed and applied *** numerical experiments,the discrete remainder vanishes and the potentials converge with the same order of accuracy as usual in other first-order partial differential *** by the successful application of the Helmholtz Hodge decomposition in theoretical plasma physics,applications to the discrete analysis of magnetohydrodynamic(MHD) wave modes are presented and discussed.

关键词： Summation by parts Vector calculus Helmholtz Hodge decomposition Mimetic properties Wave mode analysis

Enhanced energy coupling for indirect-drive fast-ignition fusion targets (vol 17, pg 435, 2020)

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NATURE PHYSICS 2020年第7期16卷 815-815页

作者： Zhang, F. Cai, H. B. Zhou, W. M. Dai, Z. S. Shan, L. Q. Xu, H. Chen, J. B. Ge, F. J. Tang, Q. Zhang, W. S. Wei, L. Liu, D. X. Gu, J. F. Du, H. B. Bi, B. Wu, S. Z. Li, J. Lu, F. Zhang, H. Zhang, B. He, M. Q. Yu, M. H. Yang, Z. H. Wang, W. W. Zhang, H. S. Cui, B. Yang, L. Wu, J. F. Qi, W. Cao, L. H. Li, Z. Liu, H. J. Yang, Y. M. Ren, G. L. Tian, C. Yuan, Z. Q. Zheng, W. D. Cao, L. F. Zhou, C. T. Zou, S. Y. Gu, Y. Q. Du, K. Ding, Y. K. Zhang, B. H. Zhu, S. P. Zhang, W. Y. He, X. T. Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center CAEP Mianyang China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) HEDPS Center for Applied Physics and Technology Peking University Beijing China (GRID:grid.11135.37) (ISNI:0000 0001 2256 9319) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) National University of Defense Technology College of Computing Science Changsha China (GRID:grid.412110.7) (ISNI:0000 0000 9548 2110) Shenzhen Technology University Center for Advanced Material Diagnostic Technology Shenzhen China (GRID:grid.499351.3) (ISNI:0000 0004 6353 6136) Science and Technology on Plasma Physics Laboratory Laser Fusion Research Center CAEP Mianyang China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132) Institute of Applied Physics and Computational Mathematics Beijing China (GRID:grid.418809.c) (ISNI:0000 0000 9563 2481) China Academy of Engineering Physics Graduate School Beijing China (GRID:grid.249079.1) (ISNI:0000 0004 0369 4132)

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

关键词： Energy science and technology Laser-produced plasmas

Nonuniform 3D finite difference elastic wave simulation on staggered grids

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arXiv 2020年

作者： Gao, Longfei Ghattas, Omar Keyes, David Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States Oden Institute for Computational Engineering and Sciences Jackson School of Geosciences Department of Mechanical Engineering The University of Texas at Austin AustinTX78712 United States Applied Mathematics and Computational Science Program Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by nonconforming interfaces. We demonstrate that this layer-wise finite difference discretization has the potential to significantly reduce the simulation cost, compared to its fully uniform counterpart. Stability of such a discretization is achieved by using specially designed difference operators, which are variants of the standard difference operators with adaptations near boundaries or interfaces, and penalty terms, which are appended to the discretized wave system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized wave system is shown to preserve the energy conserving property of the continuous elastic wave equation, and a fortiori ensure the stability of the simulation. Numerical examples are presented to demonstrate the efficacy of the proposed simulation approach. © 2020, CC BY.

关键词： Elastic waves

ParaDiag: Parallel-in-time algorithms based on the diagonalization technique

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arXiv 2020年

作者： Gander, Martin J. Liu, Jun Wu, Shu-Lin Yue, Xiaoqiang Zhou, Tao Section of Mathematics University of Geneva GenevaCH-1211 Switzerland Department of Mathematics and Statistics Southern Illinois University Edwardsville EdwardsvilleIL62026 United States School of Mathematics and Statistics Northeast Normal University Changchun130024 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing China

In 2008, Maday and Rønquist introduced an interesting new approach for the direct parallel-in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping matrix, keeping the matrices for the space discretization unchanged, and then to solve all time steps in parallel. Since then, several variants appeared, and we call these closely related algorithms ParaDiag algorithms. ParaDiag algorithms in the literature can be classified into two groups: We will explain the basic features of each group in this note. To have concrete examples, we will introduce ParaDiag-I and ParaDiag-II for the advection-diffusion equation. We will also introduce ParaDiag-II for the wave equation and an optimal control problem for the wave equation. We could have used the advection-diffusion equation as well to illustrate ParaDiag-II, but wave equations are known to cause problems for certain PinT algorithms and thus constitute an especially interesting example for which ParaDiag algorithms were tested. We show the main known theoretical results in each case, and also provide Matlab codes for testing. The goal of the Matlab codes is to help the interested reader understand the key features of the ParaDiag algorithms, without intention to be highly tuned for efficiency and/or low memory use. We also provide speedup measurements of ParaDiag algorithms for a 2D linear advection-diffusion equation. These results are obtained on the Tianhe-1 supercomputer in China and the SIUE Campus Cluster in the US, which is a multi-array, configurable and cooperative parallel system, and we compare these results to the performance of parareal and MGRiT, two widely used PinT algorithms. In a forthcoming update of this note, we will provide more material on ParaDiag algorithms, in particular further Matlab codes and parallel computing results, also for more realistic applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Advection

Shape correspondence using anisotropic Chebyshev spectral CNNs

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Shape correspondence using anisotropic Chebyshev spectral CN...

Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Qinsong Li Shengjun Liu Ling Hu Xinru Liu Institute of Engineering Modeling and Scientific Computing Central South University State Key Laboratory of High Performance Manufacturing Complex Central South University School of Mathematics and Computational Science Hunan First Normal University

ISBN: (数字)9781728171685

ISBN: (纸本)9781728171692

Establishing correspondence between shapes is a very important and active research topic in many domains. Due to the powerful ability of deep learning on geometric data, lots of attractive results have been achieved by convolutional neural networks (CNNs). In this paper, we propose a novel architecture for shape correspondence, termed Anisotropic Chebyshev spectral CNNs (ACSCNNs), based on a new extension of the manifold convolution operator. The extended convolution operators aggregate the local features of signals by a set of oriented kernels around each point, which allows to much more comprehensively capture the intrinsic signal information. Rather than using fixed oriented kernels in the spatial domain in previous CNNs, in our framework, the kernels are learned by spectral filtering, based on the eigen-decompositions of multiple Anisotropic Laplace-Beltrami Operators. To reduce the computational complexity, we employ an explicit expansion of the Chebyshev polynomial basis to represent the spectral filters whose expansion coefficients are trainable. Through the benchmark experiments of shape correspondence, our architecture is demonstrated to be efficient and be able to provide better than the state-of-the-art results in several datasets even if using constant functions as inputs.

关键词： Shape Manifolds Convolution Kernel Machine learning Eigenvalues and eigenfunctions Chebyshev approximation

An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow

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arXiv 2020年

作者： Wang, Lin Yu, Haijun School of Applied Mathematics Guangdong University of Technology GuangzhouGuangdong510006 China LSEC & NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose and analyze a linearly stabilized semi-implicit diffusive Crank–Nicolson scheme for the Cahn–Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation. Rigorous error analysis is carried out for the fully discrete scheme. When the time step-size and the space step-size are small enough, second order accuracy in time is obtained with a prefactor controlled by some lower degree polynomial of 1/Ε. Here Ε is the thickness of the interface. Numerical results together with an adaptive time stepping are presented to verify the accuracy and efficiency of the proposed scheme. Copyright © 2020, The Authors. All rights reserved.

关键词： Error analysis

Lattice studies of Sp(2N) gauge theories using GRID 40

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Lattice studies of Sp(2N) gauge theories using GRID

40th International Symposium on Lattice Field Theory, LATTICE 2023

作者： Bennett, Ed Boyle, Peter Del Debbio, Luigi Forzano, Niccolò Hong, Deog Ki Lee, Jong-Wan Lenz, Julian Lin, C.-J. David Lucini, Biagio Lupo, Alessandro Piai, Maurizio Vadacchino, Davide Swansea Academy of Advanced Computing Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom School of Physics and Astronomy University of Edinburgh EdinburghEH9 3FD United Kingdom Physics Department Brookhaven National Laboratory UptonNY11973 United States Higgs Centre for Theoretical Physics School of Physics and Astronomy The University of Edinburgh Peter Guthrie Tait Road EdinburghEH9 3FD United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park SwanseaSA2 8PP United Kingdom Department of Physics Pusan National University Busan46241 Korea Republic of Institute for Extreme Physics Pusan National University Busan46241 Korea Republic of Daejeon34126 Korea Republic of Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Centre for High Energy Physics Chung-Yuan Christian University Chung-Li32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Bay Campus Fabian Way Wales SwanseaSA1 8EN United Kingdom Centre for Mathematical Sciences University of Plymouth PlymouthPL4 8AA United Kingdom

Four-dimensional gauge theories based on symplectic Lie groups provide elegant realisations of the microscopic origin of several new physics models. Numerical studies pursued on the lattice provide quantitative information necessary for phenomenological applications. To this purpose, we implemented Sp(2N) gauge theories using Monte Carlo techniques within Grid, a performant framework designed for the numerical study of quantum field theories on the lattice. We show the first results obtained using this library, focusing on the case-study provided by the Sp(4) theory coupled to Nas = 4 Wilson-Dirac fermions transforming in the 2-index antisymmetric representation. In particular, we discuss preliminary tests of the algorithm and we test some of its main functionalities. © Copyright owned by the author(s) under the terms of the Creative Commons.

关键词： Lattice theory

Tensor network quantum virtual machine for simulating quantum circuits at exascale

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arXiv 2021年

作者： Nguyen, Thien Lyakh, Dmitry Dumitrescu, Eugene Clark, David Larkin, Jeff McCaskey, Alexander Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN United States National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN United States Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN United States NVIDIA Corp. Santa ClaraCA United States

The numerical simulation of quantum circuits is an indispensable tool for development, verification and validation of hybrid quantum-classical algorithms on near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. We present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) which serves as a quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the general purpose, scalable tensor network processing library, ExaTN, and provides multiple configurable quantum circuit simulators enabling either exact quantum circuit simulation via the full tensor network contraction, or approximate quantum state representations via suitable tensor factorizations. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical backend we introduce an end-to-end virtual quantum development environment which can scale from laptops to future exascale platforms. We report initial benchmarks of our framework which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on the Google Sycamore superconducting architecture. Copyright © 2021, The Authors. All rights reserved.

关键词： Circuit simulation

Composable Programming of Hybrid Workflows for Quantum Simulation

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Composable Programming of Hybrid Workflows for Quantum Simul...

IEEE International Conference on Software Architecture Workshops (ICSAW)

作者： Thien Nguyen Lindsay Bassman Dmitry Lyakh Alexander McCaskey Vicente Leyton-Ortega Raphael Pooser Wael Elwasif Travis S. Humble Wibe A. de Jong Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge TN USA Oak Ridge National Laboratory Quantum Computing Institute Oak Ridge TN USA Computational Research Division Lawrence Berkeley National Laboratory Berkeley California USA National Center for Computational Sciences Oak Ridge National Laboratory Oak Ridge TN USA Computer Science and Engineering Division Oak Ridge National Laboratory Oak Ridge TN USA

ISBN: (纸本)9781665439107;9781665429870

We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data structures and methods that enable programming of a broad variety of complex hybrid quantum simulation applications. The abstract core of our scheme is distilled from the analysis of the current quantum simulation algorithms. Subsequently, it allows a synthesis of new hybrid algorithms and workflows via the extension, specialization, and dynamic customization of the abstract core classes defined by our design. We implement our design scheme using the hardware-agnostic programming language QCOR into the QuaSiMo library. To validate our implementation, we test and show its utility on commercial quantum processors from IBM, running some prototypical quantum simulations.

关键词： Program processors Heuristic algorithms Object oriented modeling Stationary state Fault tolerant systems Programming Libraries

Hybrid deep learning and isogeometric analysis for bearing capacity assessment of sand over clay

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Journal of Rock Mechanics and Geotechnical engineering 2024年

作者： Toan Nguyen-Minh Tram Bui-Ngoc Jim Shiau Tan Nguyen Trung Nguyen-Thoi Faculty of Civil Engineering Ton Duc Thang University Ho Chi Minh City 700000 Vietnam Laboratory for Computational Mechanics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City 700000 Vietnam Faculty of Mechanical - Electrical and Computer Engineering School of Technology Van Lang University Ho Chi Minh City 700000 Vietnam School of Engineering University of Southern Queensland Toowoomba QLD 4350 Australia Smart Computing in Civil Engineering Research Group Ton Duc Thang University Ho Chi Minh City 700000 Vietnam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial Intelligence Van Lang University Ho Chi Minh City 700000 Vietnam

In this paper, Isogeometric analysis (IGA) is effectively integrated with machine learning (ML) to investigate the bearing capacity of strip footings in layered soil profiles, with a focus on a sand-over-clay configuration. The study begins with the generation of a comprehensive dataset of 10,000 samples from IGA upper bound (UB) limit analyses, facilitating an in-depth examination of various material and geometric conditions. A hybrid deep neural network, specifically the Whale Optimization Algorithm-Deep Neural Network (WOA-DNN), is then employed to utilize these 10,000 outputs for precise bearing capacity predictions. Notably, the WOA-DNN model outperforms conventional ML techniques, offering a robust and accurate prediction tool. This innovative approach explores a broad range of design parameters, including sand layer depth, load-to-soil unit weight ratio, internal friction angle, cohesion, and footing roughness. A detailed analysis of the dataset reveals the significant influence of these parameters on bearing capacity, providing valuable insights for practical foundation design. This research demonstrates the usefulness of data-driven techniques in optimizing the design of shallow foundations within layered soil profiles, marking a significant stride in geotechnical engineering advancements.

关键词： UB limit analysis Isogeometric analysis (IGA) hybrid deep neural network Whale optimization algorithm