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The role of isotropic and anisotropic Hubbard corrections for the magnetic ordering and absolute band alignment of hematite α-Fe2O3（0001）surfaces

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Progress in Natural Science:Materials International 2019年第3期29卷 349-355页

作者： Sateesh Bandaru Ivan Scivetti Chi-Yung Yam Gilberto Teobaldi School of Chemical and Bioprocess Engineering University College Dublin Beijing Computational Science Research Center Stephenson Institute for Renewable Energy Department of ChemistryThe University of Liverpool Scientific Computing Department Science and Technology Facilities CouncilDaresbury Laboratory

An isotropic （+U） and anisotropic [+（U-J）] corrected Density Functional Theory study for bulk hematite （α-Fe2O3） was carried out,and several competing terminations of its （0001） surface modeled via slabs of increasing thickness from twelve to thirty-six *** spite of small quantitative differences,the use of either U or （U-J）corrections showed not to qualitatively affect the results of the simulations both for bulkα-Fe2O3and the lowestenergyα-Fe2O3（0001） surface studied,regardless of the thickness of the slab *** energy favored antiferromagnetic ordering of bulkα-Fe2O3was preserved in the relaxed slabs,with the largest surface-induced effects limited to the outermost three Fe-layers in the *** O-and Fe-terminations were found to be energetically favored and ***,fully O-or Fe-terminated surfaces were calculated to be energetically disfavored and ***,the role of Fe-or O-termination for the semiconducting or metallic nature as well as absolute band alignment ofα-Fe2O3（0001） surfaces was analyzed and discussed with respect to the challenges in enhancing the activity ofα-Fe2O3samples as photo-electrode for water splitting.

关键词： Hematite α-Fe2O3 Surfaces Photo-electrodes Density functional theory Electronic properties Magnetic properties

A polyconvex transversely-isotropic invariant-based formulation for electro-mechanics: stability, minimisers and computational implementation

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arXiv 2022年

作者： Horák, Martin Gil, Antonio J. Ortigosa, Rogelio Kružík, Martin Faculty of Civil Engineering Czech Technical University Thákurova 7 Praha 6CZ-166 29 Czech Republic Zienkiewicz Centre for Computational Engineering Faculty of Science and Engineering Swansea University Bay Campus SA1 8EN United Kingdom Computational Mechanics and Scientific Computing Group Technical University of Cartagena Campus Muralla del Mar Cartagena Murcia30202 Spain Czech Academy of Sciences Institute of Information Theory and Automation Pod vodárenskou věží 4 Praha 8CZ-182 00 Czech Republic

The fabrication of evermore sophisticated miniaturised soft robotic components made up of Electro-Active Polymers (EAPs) is constantly demanding parallel development from the in-silico simulation point of view. The incorporation of crystallographic anisotropic micro-architectures, within an otherwise nearly uniform isotropic soft polymer matrix, has shown great potential in terms of advanced three-dimensional actuation (i.e. stretching, bending, twisting), especially at large strains, that is, beyond the onset of geometrical pull-in instabilities. To accommodate for this in-silico response, this paper presents a phenomenological invariant-based polyconvex transversely isotropic framework for the simulation of EAPs at large strains. This research expands previous work developed by Gil and Ortigosa for isotropic EAPs [40] with the help of the pioneering work by Schröeder and Neff [81] in the context of polyconvexity for materials endowed with crystallographic architectures in single physics mechanics. The paper also summarises key important results both in terms of the existence of minimisers and material stability. In addition, a series of numerical examples is presented in order to demonstrate the effect that the anisotropic orientation and the contrast of material properties, as well as the level of deformation and electric field, have upon the response of the EAP when subjected to large three-dimensional stretching, bending and torsion, including the possible development of wrinkling. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

Finite Element Method for a Nonlinear PML Helmholtz Equation with High Wave Number

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arXiv 2022年

作者： Jiang, Run Li, Yonglin Wu, Haijun Zou, Jun Department of Mathematics Nanjing University Jiangsu210093 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Hong Kong Department of Mathematics The Chinese University of Hong Kong N.T. Shatin Hong Kong

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM). Wave-number-explicit stability and regularity estimates and the exponential convergence are proved for the nonlinear truncated PML problem. Preasymptotic error estimates are obtained for the FEM, where the logarithmic factors in h required by the previous results for the NLH with impedance boundary condition are removed in the case of two dimensions. Moreover, local quadratic convergences of the Newton's methods are derived for both the NLH with PML and its FEM. Numerical examples are presented to verify the accuracy of the FEM, which demonstrate that the pollution errors may be greatly reduced by applying the interior penalty technique with proper penalty parameters to the FEM. The nonlinear phenomenon of optical bistability can be successfully simulated. Copyright © 2022, The Authors. All rights reserved.

关键词： Finite element method

Quadrature Sampling of Parametric Models with Bi-fidelity Boosting

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arXiv 2022年

作者： Cheng, Nuojin Malik, Osman Asif Xu, Yiming Becker, Stephen Doostan, Alireza Narayan, Akil Department of Applied Mathematics University of Colorado Boulder United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory United States Corporate Model Risk Wells Fargo United States Smead Aerospace Engineering Sciences Department University of Colorado Boulder United States Scientific Computing and Imaging Institute Department of Mathematics University of Utah United States

Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise to reduce the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bi-fidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the non-boosted solution. Copyright © 2022, The Authors. All rights reserved.

关键词： Random errors

Application of a dispersive wave hydro-sediment-morphodynamic model in the Ria Formosa lagoon

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arXiv 2022年

作者： Kazhyken, Kazbek Valseth, Eirik Videman, Juha Dawson, Clint Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States CAMGSD Departamento de Matemática Universidade de Lisboa Lisbon1049-001 Portugal Department of Data Science The Norwegian University of Life Sciences Ås1433 Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo0164 Norway

Results of an application of a dispersive wave hydro-sediment-morphodynamic model in the western circulation cell of the Ria Formosa lagoon located in the Algarve region of the southern Portugal are presented. This area of interest has a couple of features that complicate the application of the dispersive wave model: (1) the area has a complex irregular geometry with a number of barrier islands that separate the lagoon from the Atlantic Ocean, artificial and naturally occurring tidal inlets, and a number of curling channels inside the lagoon that interconnect the inlets and serve as waterways between the lagoon settlements;(2) the tidal range in the area can reach up to 3.5 m;therefore, the terrain inside the lagoon is characterized by vast salt marshes and tidal flats, and the wetting-drying process is a key component of any hydrodynamic simulation in this area. A model representation of the area has been developed by generating an unstructured finite element mesh of the circulation cell, and collecting data on parameters that characterize the tidal waves in the area, and bottom friction and sediment transport models used in the simulations. The results of the simulations indicate that the dispersive wave model can be applied in coastal areas with nontrivial underlying physical processes, and complex irregular geometries. Moreover, the dispersive term of the model is capable of capturing additional flow characteristics that are otherwise not present in hydrodynamic simulations that involve the nonlinear shallow water equations;and these additional flow features can, in their turn, affect the resulting sediment transport and bed morphodynamic process simulations. Copyright © 2022, The Authors. All rights reserved.

关键词： Equations of motion

Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems

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arXiv 2022年

作者： Malik, Osman Asif Xu, Yiming Cheng, Nuojin Becker, Stephen Doostan, Alireza Narayan, Akil Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory United States Corporate Model Risk Wells Fargo United States Department of Applied Mathematics University of Colorado Boulder United States Smead Aerospace Engineering Sciences Department University of Colorado Boulder United States Scientific Computing and Imaging Institute Department of Mathematics University of Utah United States

Approximate solutions to large least squares problems can be computed efficiently using leverage score-based row-sketches, but directly computing the leverage scores, or sampling according to them with naive methods, still requires an expensive manipulation and processing of the design matrix. In this paper we develop efficient leverage score-based sampling methods for matrices with certain Kronecker product-type structure;in particular we consider matrices that are monotone lower column subsets of Kronecker product matrices. Our discussion is general, encompassing least squares problems on infinite domains, in which case matrices formally have infinitely many rows. We briefly survey leverage score-based sampling guarantees from the numerical linear algebra and approximation theory communities, and follow this with efficient algorithms for sampling when the design matrix has Kronecker-type structure. Our numerical examples confirm that sketches based on exact leverage score sampling for our class of structured matrices achieve superior residual compared to approximate leverage score sampling methods. Copyright © 2022, The Authors. All rights reserved.

关键词： Least squares approximations

A MULTIFIDELITY MONTE CARLO METHOD FOR REALISTIC computational BUDGETS

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arXiv 2022年

作者： Gruber, Anthony Gunzburger, Max Ju, Lili Wang, Zhu Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseeFL32306 United States Oden Institute for Computational Engineering and Sciences University of Texas at Austin 201 E 24th Street AustinTX78712 United States Department of Mathematics University of South Carolina 1523 Greene Street ColumbiaSC29208 United States

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo *** Codes 62K05, 49M20 Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

An Energy-Stable Finite Element Method for Nonlinear Maxwell's Equations

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SSRN

SSRN 2022年

作者： Li, Lingxiao Lyu, Maohui Zheng, Weiying School of Mathematics and Statistics Henan University Kaifeng475004 China Center for Applied Mathematics of Henan Province Henan University Zhengzhou450046 China LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

In this paper, we consider the three-dimensional (3D) nonlinear Maxwell’s equations in an optical medium characterized by the linear Lorentz dispersion, the nonlinear Kerr effect, and the delayed Raman scattering. By introducing auxiliary variables, we propose a fully-discrete and energy-stable finite element method for the nonlinear problem. The discrete scheme is unconditionally stable and admits second-order convergence. To solve the nonlinear discrete problem, we propose a Newton-Krylov iterative method, where the linearized algebraic problems are solved with a preconditioned GMRES method based on the auxiliary space preconditioning for Maxwell’s equations. Numerical experiment for a spatial soliton shows agreements with the two-dimensional numerical simulations in the literature. Moreover, we also demonstrate the efficiency and parallel scalability of the finite element method numerically on 1–512 computer processors. © 2022, The Authors. All rights reserved.

关键词： Finite element method

A NITSCHE HYBRID MULTISCALE METHOD WITH NON-MATCHING GRIDS

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arXiv 2021年

作者： 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 propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic problem with bounded and measurable coefficients. The rate of convergence may be derived for coefficients with further structures such as periodicity and ergodicity. Extensive numerical results confirm the theoretical predictions. Copyright © 2021, The Authors. All rights reserved.

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