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arXiv 2020年

作者： Zhang, Yongwei Ma, Chupeng Cao, Liqun Shi, Dongyang School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China Institute for Applied Mathematics Interdisciplinary Center for Scientific Computing Heidelberg University Im Neuenheimer Feld 205 Heidelberg69120 Germany LSEC NCMIS University of Chinese Academy of Sciences Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we consider numerical simulations of the nonlocal optical response of metallic nanostructure arrays inside a dielectric host, which is of particular interest to the nanoplasmonics community due to many unusual properties and potential applications. mathematically, it is described by Maxwell’s equations with discontinuous coefficients coupled with a set of Helmholtz-type equations defined only on the domains of metallic nanostructures. To solve this challenging problem, we develop an efficient multiscale method consisting of three steps. First, we extend the system into the domain occupied by the dielectric medium in a novel way and result in a coupled system with rapidly oscillating coefficients. A rigorous analysis of the error between the solutions of the original system and the extended system is given. Second, we derive the homogenized system and define the multiscale approximate solution for the extended system by using the multiscale asymptotic method. Third, to fix the inaccuracy of the multiscale asymptotic method inside the metallic nanostructures, we solve the original system in each metallic nanostructure separately with boundary conditions given by the multiscale approximate solution. A fast algorithm based on the LU decomposition is proposed for solving the resulting linear systems. By applying the multiscale method, we obtain the results that are in good agreement with those obtained by solving the original system directly at a much lower computational cost. Numerical examples are provided to validate the efficiency and accuracy of the proposed method. Copyright © 2020, The Authors. All rights reserved.

关键词： Finite element method

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On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

arXiv

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arXiv 2021年

作者： Guermond, Jean-Luc Kronbichler, Martin Maier, Matthias Popov, Bojan Tomas, Ignacio Department of Mathematics Texas A&M University 3368 College StationTX77843 United States Institute for Computational Mechanics Department for Mechanical Engineering Technical University of Munich Germany Division of Scientific Computing Department of Information Technology Uppsala University Sweden Sandia National Laboratories P.O. Box 5800 MS 1320 AlbuquerqueNM87185-1320 United States

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is second-order accurate in time and space. Robustness here means that the method is proved to be invariant domain preserving under the hyperbolic CFL time step restriction, and the method delivers results that are reproducible. The proposed technique is shown to be accurate on challenging 2D and 3D realistic *** Codes 35L65, 65M60, 65M12, 65N30 Copyright © 2021, The Authors. All rights reserved.

关键词： Finite element method

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Optimal network slicing for service-oriented networks with flexible routing and guaranteed E2E latency

arXiv

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arXiv 2020年

作者： Chen, Wei-Kun Liu, Ya-Feng de Domenico, Antonio Luo, Zhi-Quan Dai, Yu-Hong The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Huawei Technologies Co. Ltd France Research Center Boulogne-Billancourt92100 France The Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China

Network function virtualization is a promising technology to simultaneously support multiple services with diverse characteristics and requirements in the 5G and beyond networks. In particular, each service consists of a predetermined sequence of functions, called service function chain (SFC), running on a cloud environment. To make different service slices work properly in harmony, it is crucial to appropriately select the cloud nodes to deploy the functions in the SFC and flexibly route the flow of the services such that these functions are processed in the order defined in the corresponding SFC, the end-to-end (E2E) latency constraints of all services are guaranteed, and all cloud and communication resource budget constraints are respected. In this paper, we first propose a new mixed binary linear program (MBLP) formulation of the above network slicing problem that optimizes the system energy efficiency while jointly considers the E2E latency requirement, resource budget, flow routing, and functional instantiation. Then, we develop another MBLP formulation and show that the two formulations are equivalent in the sense that they share the same optimal solution. However, since the numbers of variables and constraints in the second problem formulation are significantly smaller than those in the first one, solving the second problem formulation is more computationally efficient especially when the dimension of the corresponding network is large. Numerical results demonstrate the advantage of the proposed formulations compared with the existing ones. Copyright © 2020, The Authors. All rights reserved.

关键词： Network function virtualization

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Recent development on some numerical methods for stochastic partial differential equations

Recent development on some numerical methods for stochastic ...

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第十六届全国微分方程数值方法暨第十三届全国仿真算法学术会议

作者：洪佳林 LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

In this talk we review our recent results on some important numerical issues for stochastic partial differential equations,inclusive of numerical stability,exponential integrability,invariant measure,numerical ergodic...

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An efficient online-offline method for elliptic homogenization problems

arXiv

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arXiv 2020年

作者： Huang, Yufang Ming, Pingbing Song, Siqi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences No. 55 East Road Zhong-Guan-Cun Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the input data for the online computation. The accuracy of the proposed method are analyzed with the aid of the refined estimates of the reconstruction operator. Two dimensional and three dimensional numerical tests confirm the efficiency of the proposed method, and illustrate that this online-offline strategy may significantly reduce the cost without loss of accuracy. Copyright © 2020, The Authors. All rights reserved.

关键词： Numerical methods

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An a posteriori error estimator for the spectral fractional power of the Laplacian

arXiv

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arXiv 2022年

作者： Bulle, Raphaël Barrera, Olga Bordas, Stéphane P.A. Chouly, Franz Hale, Jack S. Institute of Computational Engineering University of Luxembourg 6 Avenue de la Fonte Esch-sur-Alzette4362 Luxembourg Université Bourgogne Franche-Comté Institut de Mathématiques de Bourgogne Dijon21078 France Center for Mathematical Modeling Department of Mathematical Engineering University of Chile IRL 2807 - CNRS Santiago Chile School of Engineering Computing and Mathematics Oxford Brookes University Oxford United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Departamento de Ingenería Matématica CI2MA Universidad de Concepción Casilla 160-C Concepción Chile

We develop a novel a posteriori error estimator for the L2 error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using rational approximations which allow to reformulate the fractional problem into a family of non-fractional parametric problems. The estimator involves applying the implicit Bank-Weiser error estimation strategy to each parametric non-fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. In addition we propose an algorithm to adapt both the finite element mesh and the rational scheme in order to balance the discretization errors. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement *** Codes 65N15, 65N30 © 2022, CC BY-NC-ND.

关键词： Finite element method

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Benchmark computations for the polarization tensor characterization of small conducting objects

arXiv

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arXiv 2021年

作者： Amad, A.A.S. Ledger, Paul D. Betcke, T. Praetorius, D. Zienkiewicz Centre for Computational Engineering College of Engineering Swansea University Bay Campus Fabian Way SwanseaSA1 8EN United Kingdom School of Computing & Mathematics Keele University Newcastle under Lyme StaffordshireST5 5BG United Kingdom Centre for Inverse Problems University College London Gower Street LondonWC1E 6BT United Kingdom TU Wien Institute for Analysis and Scientific Computing Wiedner Hauptstr. 8-10 / E101 / 4 Wien1040 Austria

The characterisation of small low conducting inclusions in an otherwise uniform background from low-frequency electrical field measurements has important applications in medical imaging using electrical impedance tomography as well as in geological imaging using electrical resistivity tomography. It is known that such objects can be characterised by a Póyla-Szegö (polarizability) tensor. Such characterisations have attracted interest as they can provide object features in a machine learning classification algorithm and provide an alternative imaging solution. However, to be able train machine learning algorithms, large dictionaries are required and it is essential that the characterisations are accurate. In this work, we obtain accurate numerical approximations to the tensor coefficients, by applying an adaptive boundary element method. The goal being to provide a sequence of benchmark computations for the tensor coefficients to allow other software developers check the accuracy of their *** Codes 65N30, 35R30, 35B30 © 2021, CC BY.

关键词： Boundary element method

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PIRA: Performance instrumentation refinement automation 5

PIRA: Performance instrumentation refinement automation

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5th ACM SIGPLAN International Workshop on Artificial Intelligence and Empirical Methods for Software engineering and Parallel computing Systems, AI-SEPS 2018, c-located with the ACM SIGPLAN Conference on Systems, Programming, Languages and Applications: Software for Humanity, SPLASH 2018

作者： Lehr, Jan-Patrick Hück, Alexander Bischof, Christian Institute for Scientific Computing Graduate School of Computational Engineering Technische Universität Darmstadt Darmstadt Germany

ISBN: (纸本)9781450360678

In this paper we present PIRA - an infrastructure for automatic instrumentation refinement for performance analysis. It automates the generation of an initial performance overview measurement and gradually refines it, based on the recorded runtime information. This can help a performance analyst with the time consuming and largely manual, yet mechanical, task of selecting which functions to capture in subsequent measurements. PIRA implements an existing aggregation strategy that heuristically determines which functions to include for initial overview measurements. Moreover, it implements a newly developed heuristic to incorporate profile information and expand instrumentation in hot-spot regions only. The approach is evaluated on different benchmarks, including the SU2 multi-physics solver package. PIRA is able to generate instrumentation configurations that contain the application's hot-spot, but generate significantly less overhead when compared to the Score-P reference measurement. © 2018 held by the owner/author(s).

关键词： Automation

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Adaptive finite element approximation for steady-state poisson-nernst-planck equations

arXiv

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arXiv 2020年

作者： Hao, Tingting Ma, Manman Xu, Xuejun School of Mathematical Sciences Tongji University Shanghai200092 China School of Mathematical Sciences Tongji University Shanghai200092 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a key contribution, the steady-state Poisson-Nernst-Planck equations are studied systematically and rigorous analysis for a residual-based a posteriori error estimate of the nonlinear system is presented. With the help of Schauder fixed point theorem, we show the solution existence and uniqueness of the linearized system derived by taking G−derivatives of the nonlinear system, followed by the proof of the relationship between the error of solution and the a posteriori error estimator η. Numerical experiments are given to validate the efficiency of the a posteriori error estimator and demonstrate the expected rate of convergence. In the further tests, adaptive mesh refinements for geometrical singularities and boundary layer effects are successfully observed. Copyright © 2020, The Authors. All rights reserved.

关键词： Nonlinear systems

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Mixed frameworks and structure preserving integration for coupled electro-elastodynamics

Mixed frameworks and structure preserving integration for co...

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90th Annual Meeting of the International Association of Applied mathematics and Mechanics, GAMM 2019

作者： Franke, Marlon Ortigosa, Rogelio Janz, Alexander Gil, Antonio J. Betsch, Peter Karlsruhe Institute of Technology Institute of Mechanics Otto-Ammann-Platz 9 Karlsruhe76131 Germany Technical University of Cartagena Computational Mechanics & Scientific Computing Group Cartagena30202 Spain Swansea University Zienkiewicz Centre for Computational Engineering Fabian Way SwanseaSA1 8EN United Kingdom

In the present contribution new approaches for the design of structure preserving time integrators for nonlinear coupled problems are proposed. Polyconvexity inspired energy functionals are obtained by using the rediscovered tensor cross product which greatly simplifies the algebra, see [1]. In this connection an extended kinematic set, consisting of the right CauchyGreen tensor, its co-factor and its Jacobian, is introduced. On this basis coupled problems like e.g. non-linear thermoelastodynamics, see [2] or electro-elastodynamics, see [3], can be considered. Furthermore the formulations are readily extendible for mixed Hu-Washizu type formulations where the extended kinematic set is introduced as unknown field. In particular in [1] an elegant cascade system of kinematic constraints was introduced for elastodynamics, crucial for the satisfaction of the required conservation properties of a new family of energy momentum (EM) consistent time integrators. The objective of the present contribution is the introduction of new mixed variational principles for EM consistent time integrators in electro-elastodynamics, hence bridging the gap between the previous works [3] and [1], opening the possibility to a variety of new finite element implementations, see [4]. The following characteristics of the proposed EM consistent time integrator make it very appealing: (i) the new family of time integrators can be shown to be thermodynamically consistent and second order accurate;(ii) piecewise discontinuous interpolation of the mixed fields is carried out in order to obtain a computational cost comparable to that of standard displacement, electric potential formulations. Eventually, the superior numerical performance of the proposed formulation is demonstrated. © 2019 The Authors Proceedings in Applied mathematics & Mechanics published by Wiley-VCH Verlag GmbH & Co. KGaA Weinheim.

关键词： Kinematics

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