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Joint design of hybrid beamforming and reflection coefficients in RIS-aided mmWave MIMO systems

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arXiv 2022年

作者： Li, Renwang Guo, Bei Tao, Meixia Liu, Ya-Feng Yu, Wei Department of Electronic Engineering Shanghai Jiao Tong University Shanghai China 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 Department of Electrical and Engineering University of Toronto TorontoONM5S 3G4 Canada

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under the signalto-interference-plus-noise ratio (SINR) constraints at all users. The problem is highly challenging to solve due to the nonconvex SINR constraints as well as the unit-modulus phase shift constraints for both the RIS reflection coefficients and the analog beamformer. A two-layer penalty-based algorithm is proposed to decouple variables in SINR constraints, and manifold optimization is adopted to handle the non-convex unitmodulus *** also propose a low-complexity sequential optimization method, which optimizes the RIS reflection coefficients, the analog beamformer, and the digital beamformer sequentially without iteration. Furthermore, the relationship between the power minimization problem and the max-min fairness (MMF) problem is discussed. Simulation results show that the proposed penalty-based algorithm outperforms the stateof-the-art semidefinite relaxation (SDR)-based algorithm. Results also demonstrate that the RIS plays an important role in the power reduction. Copyright © 2022, The Authors. All rights reserved.

关键词： Millimeter waves

GENERALIZED TRUNCATED MOMENT PROBLEMS WITH UNBOUNDED SETS

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arXiv 2022年

作者： Huang, Lei Nie, Jiawang Yuan, Ya-Xiang Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics University of California 9500 Gilman Drive La Jolla San DiegoCA92093 United States Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100049 China

This paper studies generalized truncated moment problems with unbounded sets. First, we study geometric properties of the truncated moment cone and its dual cone of nonnegative polynomials. By the technique of homogenization, we give a convergent hierarchy of Moment-SOS relaxations for approximating these cones. With them, we give a Moment-SOS method for solving generalized truncated moment problems with unbounded sets. Finitely atomic representing measures, or certificates for their nonexistence, can be obtained by the proposed method. Numerical experiments and applications are also given. Copyright © 2022, The Authors. All rights reserved.

关键词： Polynomials

IMPROVED LAGUERRE SPECTRAL METHODS WITH LESS ROUND-OFF ERRORS AND BETTER STABILITY

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arXiv 2022年

作者： Huang, Shenghe Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight e−x. They have wide applications in scientific and engineering computations. However, the exponential growth of Laguerre polynomials of high degree makes it hard to apply them to complicated systems that need to use large numbers of Laguerre bases. In this paper, we introduce modified three-term recurrence formula to reduce the round-off error and to avoid overflow and underflow issues in generating generalized Laguerre polynomials and Laguerre functions. We apply the improved Laguerre methods to solve an elliptic equation defined on the half line. More than one thousand Laguerre bases are used in this application and meanwhile accuracy close to machine precision is achieved. The optimal scaling factor of Laguerre methods are studied and found to be independent of number of quadrature points in two cases that Laguerre methods have better convergence speeds than mapped Jacobi *** Codes 65N35, 65D32, 65G50, 33F05 © 2022, CC BY-NC-ND.

关键词： Polynomials

Stress-constrained topology optimization of lattice-like structures using component-wise reduced order models

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arXiv 2022年

作者： McBane, Sean Choi, Youngsoo Willcox, Karen Oden Institute for Computational Engineering & Sciences University of Texas AustinTX78712 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This computational expense may be particularly burdensome in many-query applications, such as optimization. We develop a stress-constrained topology optimization method for lattice-like structures that uses component-wise reduced order models as a cheap surrogate, providing accurate computation of stress fields while greatly reducing run time relative to a full order model. We demonstrate the ability of our method to produce large reductions in mass while respecting a constraint on the maximum stress in a pair of test problems. The ROM methodology provides a speedup of about 150x in forward solves compared to full order static condensation and provides a relative error of less than 5% in the relaxed stress. Copyright © 2022, The Authors. All rights reserved.

关键词： Constrained optimization

Disconnection Flow-Mediated Grain Rotation

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arXiv 2023年

作者： Qiu, Caihao Salvalaglio, Marco Srolovitz, David J. Han, Jian Department of Materials Science and Engineering City University of Hong Kong Hong Kong Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany Department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong

Interface migration in microstructures is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a continuum model for arbitrarily-curved grain boundaries or heterophase interfaces accounting for disconnections’ role in grain rotation. Numerical simulations show that their densities evolve as grain size and shape change, generating stresses and increasing or decreasing misorientation;the predictions agree with molecular dynamics simulations for pure capillarity-driven evolution, and are interpreted through an extended Cahn-Taylor model. Copyright © 2023, The Authors. All rights reserved.

关键词： Molecular dynamics

A Dynamic Pyramidal Relaxation Method of AC OPF

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A Dynamic Pyramidal Relaxation Method of AC OPF

Power and Electrical engineering (ACPEE), 5th Asia Conference on

作者： Yu-Yang Tang Liang Chen Hongbo Du Sheng-Jie Chen Caixia Kou Xiaomeng Ai Bo Zhou Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Computational Mathematics and Scientific/Engineering Computing Beijing China College of Sciences Beijing University of Posts and Telecommunications Beijing China Academy of Mathematics and Systems Science Chinese Academy of Sciences Institute of Applied Mathematics Beijing China School of Electrical and Electronic Engineering Huazhong University of Science and Technology Wuhan China Department of Industrial and Operations Engineering University of Michigan Ann Arbor United States

ISBN: (数字)9798350309638

ISBN: (纸本)9798350309645

The Alternating Current Optimal Power Flow (AC OPF) is crucial for power system analysis, yet existing algorithms face challenges in meeting the diverse requirements of practical applications. This paper presents a Pyramidal Relaxation (PR) formulation of the Branch Flow Model (BFM) for AC OPF, where surface conical constraints are approximated through a union of tetrahedrons in a Mixed Integer Linear Programming (MILP) relaxation. To reduce problem size and to enhance computational efficiency, we proposed a Dynamic Pyramidal Relaxation (DPR) method, where the cuts (inner approximation and outer approximation) are adaptively added. In practice, the DPR method is embedded into a MILP commercial solver based on the branch-and-cut framework. Case studies in different test systems validate the effectiveness in terms of feasibility, accuracy, and efficiency of our proposed method.

关键词： Electrical engineering computational modeling Power system dynamics Asia Linear approximation Relaxation methods Mixed integer linear programming

Semi-implicit energy-preserving numerical schemes for stochastic wave equation via SAV approach

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arXiv 2022年

作者： Cui, Jianbo Hong, Jialin Sun, Liying Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV) schemes, are constructed by transforming the considered SWE into a higher dimensional stochastic system with a stochastic SAV. We prove that they can be solved explicitly and preserve the modified energy evolution law and the regularity structure of the original system. These structure-preserving properties are the keys to overcoming the mutual effect of the noise and nonlinearity. By proving new regularity estimates of the introduced SAV, we establish the strong convergence rate of stochastic SAV schemes and the further fully-discrete schemes with the finite element method in spatial direction. To the best of our knowledge, this is the first result on the construction and strong convergence of semi-implicit energy-preserving schemes for nonlinear SWE. © 2022, CC BY.

关键词： Stochastic systems

Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China mathematics 2021年第5期64卷 887-902页

作者： Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope *** first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step *** we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)<***,with a novel discrete orthogonal convolution kernels argument and some new estimates on the corresponding positive definite quadratic forms,the L^(2)norm stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis

Force-based gradient descent method for ab initio atomic structure relaxation

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Physical Review B 2022年第10期106卷 104101-104101页

作者： Yukuan Hu Xingyu Gao Yafan Zhao Xin Liu Haifeng Song State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of Sciences Beijing 100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China CAEP Software Center for High Performance Numerical Simulation Beijing 100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial step size capturing the local curvature of the energy surface. The exit is controlled by a nonrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only three parameters are present without tuning.

关键词： Crystal structure Structural properties Density functional theory development