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arXiv 2022年

作者： Kim, Alex G. Palmese, Antonella Pereira, Maria E.S. Aldering, Greg Andrade-Oliveira, Felipe Annis, James Bailey, Stephen BenZvi, Segev Braga-Neto, Ulysses Courbin, Frédéric Garcia, Alyssa Jeffery, David Narayan, Gautham Perlmutter, Saul Soares-Santos, Marcelle Treu, Tommaso Wang, Lifan Aguiar, Odylio D. Akrami, Yashar Birrer, Simon Bom, Clécio R. Buckley-Geer, Elizabeth Cabuk, Nazim Cabuk, Senem Cadonati, Laura Caliskan, Mesut Chen, Thomas Y. Davis, Tamara M. Eskilt, Johannes R. Esteves, Johnny Ferraro, Simone Fisher, Robert Gamezo, Vadim N. García-Bellido, Juan Gill, Mandeep S.S. Herner, Kenneth Huterer, Dragan Ishak, Mustapha Iyer, Bala Jin, Shang-Jie Kilpatrick, Charles D. Koopmans, Léon V.E. Lagos, Macarena Lahav, Ofer Makler, Martín Nugent, Peter Nunes, Rafael C. Poludnenko, Alexei Y. Radice, David Rao, Suvrat Santana-Silva, Luidhy Sasaki, Misao Sathyaprakash, Bangalore Shafieloo, Arman Shao, Lijing Sherman, Nora Singh, Rajeev Smith, Joshua Tohuvavohu, Aaron Physics Division Lawrence Berkeley National Laboratory Berkeley94720 CA United States Department of Physics University of California Berkeley 366 LeConte Hall MC 7300 BerkeleyCA94720 United States NASA Einstein Germany Hamburger Sternwarte Universität Hamburg Gojenbergsweg 112 Hamburg21029 Germany Department of Physics University of Michigan Ann ArborMI48109 United States Fermi National Accelerator Laboratory P. O. Box 500 BataviaIL60510 United States Department of Physics and Astronomy University of Rochester RochesterNY14627 United States Department of Physics and Astronomy Texas A&M University College StationTX77845 United States Observatoire de Sauverny Versoix1290 Switzerland Department of Physics and Astronomy University of Nevada United States University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Physics and Astronomy University of California Los AngelesCA90095-1547 United States Instituto Nacional de Pesquisas Espaciais São José dos Campos São Paulo12227-010 Brazil CERCA ISO Department of Physics Case Western Reserve University 10900 Euclid Avenue ClevelandOH44106 United States Department of Physics Imperial College London Blackett Laboratory Prince Consort Road LondonSW7 2AZ United Kingdom Laboratoire de Physique de l'École Normale Supérieure ENS Université PSL CNRS Sorbonne Université Université de Paris ParisF-75005 France Kavli Institute for Particle Astrophysics and Cosmology Department of Physics Stanford University StanfordCA94305 United States Centro Brasileiro de Pesquisas Físicas Rua Dr. Xavier Sigaud 150 RJ Rio de JaneiroCEP 22290-180 Brazil Department of Astronomy and Astrophysics University of Chicago ChicagoIL60637 United States Faculty of Engineering Department of Physics Engineering Ankara University Turkey Faculty of Science Department of Astronomy and Space Sciences Ankara University Turkey Center for Relativistic Astrophysics School of Physics Georgia Inst

This invited Snowmass 2021 White Paper highlights the power of joint-analysis of astronomical transients in advancing HEP Science and presents research activities that can realize the opportunities that come with current and upcoming projects. Transients of interest include gravitational wave events, neutrino events, strongly-lensed quasars and supernovae, and Type Ia supernovae specifically. These transients can serve as probes of cosmological distances in the Universe and as cosmic laboratories of extreme strong-gravity, high-energy physics. Joint analysis refers to work that requires significant coordination from multiple experiments or facilities so encompasses Multi-Messenger Astronomy and optical transient discovery and distributed follow-up programs. Copyright © 2022, The Authors. All rights reserved.

关键词： Probes

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Accelerating large partial EVD/SVD calculations by filtered block Davidson methods

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Science China mathematics 2016年第8期59卷 1635-1662页

作者： ZHOU Yunkai WANG Zheng ZHOU Aihui Department of Mathematics Southern Methodist University LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences

Partial eigenvalue decomposition(PEVD) and partial singular value decomposition(PSVD) of large sparse matrices are of fundamental importance in a wide range of applications, including latent semantic indexing, spectral clustering, and kernel methods for machine learning. The more challenging problems are when a large number of eigenpairs or singular triplets need to be computed. We develop practical and efficient algorithms for these challenging problems. Our algorithms are based on a filter-accelerated block Davidson *** types of filters are utilized, one is Chebyshev polynomial filtering, the other is rational-function filtering by solving linear equations. The former utilizes the fastest growth of the Chebyshev polynomial among same degree polynomials; the latter employs the traditional idea of shift-invert, for which we address the important issue of automatic choice of shifts and propose a practical method for solving the shifted linear equations inside the block Davidson method. Our two filters can efficiently generate high-quality basis vectors to augment the projection subspace at each Davidson iteration step, which allows a restart scheme using an active projection subspace of small dimension. This makes our algorithms memory-economical, thus practical for large PEVD/PSVD calculations. We compare our algorithms with representative methods, including ARPACK, PROPACK, the randomized SVD method, and the limited memory SVD method. Extensive numerical tests on representative datasets demonstrate that, in general, our methods have similar or faster convergence speed in terms of CPU time, while requiring much lower memory comparing with other methods. The much lower memory requirement makes our methods more practical for large-scale PEVD/PSVD computations.

关键词： partial EVD/SVD polynomial filter rational filter kernel graph

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Positivity preserving DG schemes for a Boltzmann - Poisson model of electrons in semiconductors in curvilinear momentum coordinates

arXiv

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arXiv 2017年

作者： Morales, José A. E. Gamba, Irene M. Endeve, Eirik Hauck, Cory TU Wien Institute for Analysis and Scientific Computing University of Texas at Austin Institute for Computational Engineering and Sciences Department of Mathematics Oak Ridge National Lab Computational and Applied Mathematics Group

The work presented in this paper is related to the development of positivity preserving Discontinuous Galerkin (DG) methods for Boltzmann - Poisson (BP) computational models of electronic transport in semiconductors. We pose the Boltzmann Equation for electron transport in curvilinear coordinates for the momentum. We consider the 1D diode problem with azimuthal symmetry, which is a 3D plus time problem. We choose for this problem the spherical coordinate system p→(|p→|, μ = cosθ, φ), slightly different to the choice in previous DG solvers for BP, because its DG formulation gives simpler integrals involving just piecewise polynomial functions for both transport and collision terms. Applying the strategy of Zhang & Shu, [1], [2], Cheng, Gamba, Proft, [3], and Endeve et al. [4], we treat the collision operator as a source term, and find convex combinations of the transport and collision terms which guarantee the positivity of the cell average of our numerical probability density function at the next time step. The positivity of the numerical solution to the pdf in the whole domain is guaranteed by applying the limiters in [1], [2] that preserve the cell average but modify the slope of the piecewise linear solutions in order to make the function non - negative. In addition of the proofs of positivity preservation in the DG scheme, we prove the stability of the semi-discrete DG scheme under an entropy norm, using the dissipative properties of our collisional operator given by its entropy inequalities. The entropy inequality we use depends on an exponential of the Hamiltonian rather than the Maxwellian associated just to the kinetic energy. Copyright © 2017, The Authors. All rights reserved.

关键词： Galerkin methods

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A multi-level mixed element scheme of the two dimensional Helmholtz transmission eigenvalue problem

arXiv

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arXiv 2017年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo 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 present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangle grids. We first construct an equivalent linear mixed formulation of the transmission eigenvalue problem and then discretize it with Lagrangian finite elements of low regularities. The proposed scheme admits a natural nested discretization, based on which we construct a multi-level scheme. Optimal convergence rate and optimal computational cost can be obtained with the scheme.65N25, 65N30, 47B07 Copyright © 2017, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Stable mixed element schemes for plate models on multiply-connected domains

arXiv

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arXiv 2017年

作者： Zhang, Shuo 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 study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of H0(rot, Ω) and a Helmholtz decomposition of its dual, we develop mixed formulations of the models which are equivalent to the primal ones respectively and which are uniformly stable. A framework of designing uniformly stable finite element schemes is presented, and a specific example is given. Copyright © 2017, The Authors. All rights reserved.

关键词： Finite element method

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MINIMAL CONSISTENT FINITE ELEMENT SPACE FOR THE BIHARMONIC EQUATION ON QUADRILATERAL GRIDS

arXiv

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arXiv 2017年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise quadratic polynomials and is of minim...

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A Barzilai-Borwein conjugate gradient method

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Science China mathematics 2016年第8期59卷 1511-1524页

作者： DAI YuHong KOU CaiXia LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences School of Science Beijing University of Posts and Telecommunications

The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.

关键词： conjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence

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An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball Problem of Large Dimensions

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Journal of the Operations Research Society of China 2016年第2期4卷 167-191页

作者： Ya-Feng Liu Rui Diao Feng Ye Hong-Wei Liu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Applied Mathematics Xidian UniversityXi’an 710071China

In this paper,we consider the problem of computing the smallest enclosing ball(SEB)of a set of m balls in Rn,where the product mn is *** first approximate the non-differentiable SEB problem by its log-exponential aggregation function and then propose a computationally efficient inexact Newton-CG algorithm for the smoothing approximation problem by exploiting its special(approximate)sparsity *** key difference between the proposed inexact Newton-CG algorithm and the classical Newton-CG algorithm is that the gradient and the Hessian-vector product are inexactly computed in the proposed algorithm,which makes it capable of solving the large-scale SEB *** give an adaptive criterion of inexactly computing the gradient/Hessian and establish global convergence of the proposed *** illustrate the efficiency of the proposed algorithm by using the classical Newton-CG algorithm as well as the algorithm from Zhou et al.(Comput Optim Appl 30:147–160,2005)as benchmarks.

关键词： Smallest enclosing ball Smoothing approximation Inexact gradient Inexact Newton-CG algorithm Global convergence

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Corrigendum to: A convergent adaptive finite element method for elliptic Dirichlet boundary control problems

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IMA Journal of Numerical Analysis 2020年第1期40卷 800-800页

作者： Gong, Wei Liu, Wenbin Tan, Zhiyu Yan, Ningning National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing China The State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Institute of Computational Mathematics Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Kent Business School University of Kent Kent UK Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong SAR NCMIS Chinese Academy of Sciences Beijing China LSEC Chinese Academy of Sciences Beijing China Institute of Systems Science Chinese Academy of Sciences Beijing China

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Joint base station clustering and beamforming for non-orthogonal multicast and unicast transmission with backhaul constraints

arXiv

引用

arXiv 2017年

作者： Chen, Erkai Tao, Meixia Liu, Ya-Feng Department of Electronic Engineering Shanghai Jiao Tong University Shanghai200240 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

The demand for providing multicast services in cellular networks is continuously and fastly increasing. In this work, we propose a non-orthogonal transmission framework based on layered-division multiplexing (LDM) to support multicast and unicast services concurrently in cooperative multi-cell cellular networks with limited backhaul capacity. We adopt a two-layer LDM structure where the first layer is intended for multicast services, the second layer is for unicast services, and the two layers are superposed with different beamformers. Each user decodes the multicast message first, subtracts it, and then decodes its dedicated unicast message. We formulate a joint multicast and unicast beamforming problem with adaptive base station clustering that aims to maximize the weighted sum of the multicast rate and the unicast rate under per-BS power and backhaul constraints. To solve the problem, we first develop a branch-and-bound algorithm to find its global optimum. We then reformulate the problem as a sparse beamforming problem and propose a low-complexity algorithm based on convex-concave procedure. Simulation results demonstrate the significant superiority of the proposed LDM-based non-orthogonal scheme over orthogonal schemes in terms of the achievable multicast-unicast rate region. Copyright © 2017, The Authors. All rights reserved.

关键词： Beamforming

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