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International Conference on mathematics and Computers in Sciences and in Industry (MCSI)

作者： Antonio Pasculli Dept. of Engineering Geology (INGEO) and Member of the INDAM Research group GNCS (National Institute of Advanced Mathematics National Group of Scientific Computing) University G. D’Annunzio Chieti-Pescara Italy

ISBN: (纸本)9781538675014

The erosion of riverbeds and riverbanks depends, among other causes, both on the velocity fields and on their gradient near their boundaries, with the generation of shear stresses. The presence of sediments modifies the viscosity and, accordingly, modifies the profiles, particularly near the edges right where they are generated. Therefore, in this work, the distortion of the velocity profiles due to an imposed spatial variability of viscosity, was studied applying the computational Fluid Dynamics (CFD). In particular, as test cases, laminar and turbulent Plane Poiseuille flows, were selected. For simplicity, it was assumed that the sediment distribution and therefore the viscosity distribution was not influenced by the mixing due to velocity field. That is, the equilibrium configuration was determined as a consequence of a spatially variable distribution of viscosity. The 2D Navier-Stokes equations, in steady state conditions, were numerically solved exploiting a research software developed and discussed by the author [1]. The turbulence was considered through the RANS (Reynolds Averaged Navier Stokes) approach. The two equations k - ε models were employed. The turbulence phenomena near solid boundaries was simulated by the means of Wall-Functions. Spatial discretization was carried out using the Finite Element Method (FEM). A structured meshing with h like adaptability was developed. Then, in order to avoid velocities and pressure instabilities, the Characteristic-based split algorithm (CBS) was applied, while, in order to correctly consider incompressibility, by a numerical point of view, the Method of Artificial Compressibility (AC) was selected. Accordingly, the related CBS-AC three steps algorithm was implemented [1]. Then, some parametric numerical experiments were performed, considering a semi-implicit, approach. As was to be expected, the velocity profiles, for both laminar and turbulent were influenced by the viscosity distribution. The discussion of the ov

关键词： Mathematical model Handheld computers Finite element analysis Production Kinetic energy Viscosity

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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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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 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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Learning from learning machines: A new generation of AI technology to meet the needs of science

arXiv

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arXiv 2021年

作者： Pion-Tonachini, Luca Bouchard, Kristofer Martin, Hector Garcia Peisert, Sean Holtz, W. Bradley Aswani, Anil Dwivedi, Dipankar Wainwright, Haruko Pilania, Ghanshyam Nachman, Benjamin Marrone, Babetta L. Falco, Nicola Prabhat Arnold, Daniel Wolf-Yadlin, Alejandro Powers, Sarah Climer, Sharlee Jackson, Quinn Carlson, Ty Sohn, Michael Zwart, Petrus Kumar, Neeraj Justice, Amy Tomlin, Claire Jacobson, Daniel Micklem, Gos Gkoutos, Georgios V. Bickel, Peter J. Cazier, Jean-Baptiste Müller, Juliane Webb-Robertson, Bobbie-Jo Stevens, Rick Anderson, Mark Kreutz-Delgado, Ken Mahoney, Michael W. Brown, James B. Pattern Computer Inc. Friday HarborWA98250 United States Biosciences Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Helen Wils Neuroscience Institute Redwood Center for Theoretical Neuroscience Uc Berkeley BerkeleyCA94720 United States Doe Agile BioFoundry Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Joint BioEnergy Institute Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Bcam Basque Center for Applied Mathematics Bilbao48009 Spain Computer Science University of California Davis DavisCA95616 United States Cenic La MiradaCA90638 United States Health Informatics University of California Davis School of Medicine SacramentoCA95817 United States Berkeley Institute for Data Science University of California Berkeley BerkeleyCA94720 United States Industrial Engineering and Operations Research University of California Berkeley BerkeleyCA94720 United States Environmental & Earth Sciences Area Lawrence Berkeley National Laboratory BerkeleyCA94803 United States Nuclear Engineering University of California Berkeley BerkeleyCA94720 United States Materials Science and Technology Division Los Alamos National Laboratory Los AlamosNM87545 United States Physics Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Bioscience Division Los Alamos National Laboratory Los AlamosNM87545 United States Earth and Environmental Sciences Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Energy Technologies Area Lawrence Berkeley National Lab BerkeleyCA94803 United States Computing and Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Industrial & Systems Engineering The University of Tennessee KnoxvilleTN37996 United States Department of Computer Science University of Missouri-Saint Louis St. LouisMO63121 United

We outline emerging opportunities and challenges to enhance the utility of AI for scientific discovery. The distinct goals of AI for industry versus the goals of AI for science create tension between identifying patterns in data versus discovering patterns in the world from data. If we address the fundamental challenges associated with "bridging the gap" between domain-driven scientific models and data-driven AI learning machines, then we expect that these AI models can transform hypothesis generation, scientific discovery, and the scientific process itself. © 2021, CC BY.

关键词： Learning systems

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

arXiv

引用

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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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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Towards a mini-app for smoothed particle hydrodynamics at exascale

arXiv

引用

arXiv 2018年

作者： Guerrera, Danilo Cabezón, Rubén M. Piccinali, Jean-Guillaume Cavelan, Aurélien Ciorba, Florina M. Imbert, David Mayer, Lucio Reed, Darren Department of Mathematics and Computer Science University of Basel Switzerland University of Basel Switzerland Scientific Computing Support Swiss National Supercomputing Centre Lugano Switzerland Nextflow Software Nantes France Center for Theoretical Astrophysics and Cosmology Institute for Computational Science University of Zürich Switzerland

The smoothed particle hydrodynamics (SPH) technique is a purely Lagrangian method, used in numerical simulations of fluids in astrophysics and computational fluid dynamics, among many other fields. SPH simulations with detailed physics represent computationally-demanding calculations. The parallelization of SPH codes is not trivial due to the absence of a structured grid. Additionally, the performance of the SPH codes can be, in general, adversely impacted by several factors, such as multiple time-stepping, long-range interactions, and/or boundary conditions. This work presents insights into the current performance and functionalities of three SPH codes: SPHYNX, ChaNGa, and SPH-flow. These codes are the starting point of an interdisciplinary co-design project, SPH-EXA, for the development of an Exascale-ready SPH mini-app. To gain such insights, a rotating square patch test was implemented as a common test simulation for the three SPH codes and analyzed on two modern HPC systems. Furthermore, to stress the differences with the codes stemming from the astrophysics community (SPHYNX and ChaNGa), an additional test case, the Evrard collapse, has also been carried out. This work extrapolates the common basic SPH features in the three codes for the purpose of consolidating them into a pure-SPH, Exascale-ready, optimized, mini-app. Moreover, the outcome of this serves as direct feedback to the parent codes, to improve their performance and overall scalability. Copyright © 2018, The Authors. All rights reserved.

关键词： Hydrodynamics

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Local seismic response change following an excavation in an area located in the territory of L’Aquila city (Italy)

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AIP Conference Proceedings 2020年第1期2293卷

作者： Pasculli Antonio Mangifesta Massimo 1Department of Engineering and Geology (INGEO) University G. d’Annunzio Chieti-Pescara Italy 2Member of the INDAM Research group GNCS (National Institute of Advanced Mathematics National Group of Scientific Computing) University G. D’Annunzio Chieti-Pescara Italy 3Research fellow Department of Engineering and Geology (INGEO) University G. d’Annunzio Chieti-Pescara Italy

This article presents the results of 2D numerical simulations to estimate the change of local seismic response due to an excavation that occurred during the L’Aquila city’s earthquake (Italy) in April 2009. The modeling is an attempt to understand the very complex phenomenon produced by multiple reflections due to particular topographic and stratigraphic geometries, verifying whether the anthropic actions are able to modify or not the surface amplifications. In particular, the numerical simulations were performed considering national and international earthquakes databases, compatible to the spectral form expected at the site. The investigations were conducted with the VisualQ4M software that is a Pre & Post Processor capable to use up in the background the Quad4M calculation code for the study of 2D seismic amplifications. In the numerical context, the model was reconstructed according to the natural slopes and topographical conformations of the site and of the stratigraphic discontinuities, using a structured mesh with dimension suitable for the minimum speed of propagation of seismic waves (Vs) in order to avoid filtering or attenuations of wave propagation.

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