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finite-element methods in electronic-structure theory

COMPUTER PHYSICS COMMUNICATIONS 2001年第1期135卷 1-34页

作者： Pask, JE Klein, BM Sterne, PA Fong, CY USN Res Lab Washington DC 20375 USA Univ Calif Davis Davis CA 95616 USA Lawrence Livermore Natl Lab Livermore CA 94550 USA

We discuss the application of the finite-element (FE) method to ab initio solid-state: electronic-structure calculations. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space;produces sparse, structured matrices, enabling the effective use of iterative solution methods;and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We discuss the construction and properties of the required FE bases and develop in detail their use in the solution of the Schrodinger and Poisson equations subject to boundary conditions appropriate for a periodic solid. We present results for the Schrodinger equation illustrating the rapid, variational convergence of the method in electronic band-structure calculations. We present results for the Poisson equation illustrating the rapid convergence of the method, both pointwise and in the L-2 norm, and its linear scaling with system size in the context of a model charge-density and Si pseudo-charge-density. Finally, we discuss the application of the method to large-scale ab initio positron distribution and lifetime calculations in solids and present results for a host of systems within the range of a conventional LMTO based approach for comparison, as well as results for systems well beyond the range of the conventional approach. The largest such calculation, involving a unit cell of 4092 atoms, was shown to be well within the range of the FE approach on existing computational platforms. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： ab initio electronic-structure calculations density functional theory finite-element methods periodic boundary conditions

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finite-element methods FOR THE STREAMFUNCTION-VORTICITY EQUATIONS - BOUNDARY-CONDITION TREATMENTS AND MULTIPLY CONNECTED DOMAINS

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SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING 1988年第4期9卷 650-668页

作者： GUNZBURGER, MD PETERSON, JS UNIV CALIF LOS ALAMOS NATL LAB DIV COMMUN & COMPUTAT LOS ALAMOS NM 87545 USA

finite-element methods for the approximation of the solution of streamfunction-vorticity equations are considered. Among the issues dealt with are multiply connected domains, the use of low-order elements, the incorporation of a variety of boundary conditions into the methodology, error estimates, and the recovery of the primitive variables. Various numerical examples are also provided.

关键词： 65N30 streamfunction-vorticity finite-element methods

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finite-element methods FOR CONFORMAL-MAPPINGS

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1989年第6期26卷 1525-1533页

作者： NITSCHE, JA

Two finite-element methods for the evaluation of singular integral operators typical in the theory of conformal mappings are analyzed.

关键词： 30C30 65R20 finite-element methods conformal mappings singular integral equations

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Phenomenological model of diffuse global and regional atrophy using finite-element methods

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2006年第11期25卷 1417-1430页

作者： Camara, Oscar Schweiger, Martin Scahill, Rachael I. Crum, William R. Sneller, Beatrix I. Schnabel, Julia A. Ridgway, Gerard R. Cash, David M. Hill, Derek L. G. Fox, Nick C. UCL Dept Comp Sci Dept Med Phys & Bioengn CMIC London WCE1 6BT England UCL Inst Neurol Dementia Res Ctr London WC1N 3BG England

The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition artefac

关键词： Alzheimer's disease atlas atrophy simulation creation of validation image databases dementia design of ground truth finite-element methods magnetic resonance imaging mesh warping modelling validation

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Crashworthiness study of a subway vehicle collision accident based on finite-element methods

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INTERNATIONAL JOURNAL OF CRASHWORTHINESS 2021年第2期26卷 159-170页

作者： Wei, Liang Zhang, Lele Tong, Xin Cui, Ke Beijing Jiaotong Univ Sch Mech Elect & Control Engn Beijing Peoples R China

The investigation and reconstruction are fundamental to enable designers to improve the subway vehicle's crashworthiness. In this paper, a crashworthiness study of a subway vehicle collision accident in Beijing was conducted. Based on field investigation, the full-scale detail finite-element model, has established to calculate the dynamic behaviour of the vehicle in the accident. Then, the numerical simulation assists with the field investigation to identifying the structural weakness, which leading the injury of the occupant. Finally, an enhancement design for the structural weak point was considered to improve the vehicle crashworthiness in the same accident scenario.

关键词： Subway vehicle crashworthiness collision accident finite-element methods

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Accuracy control in the optimization of microwave devices by finite-element methods

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2002年第8期50卷 1901-1911页

作者： Gavrilovic, MM Webb, JP EMS Technol Ste Anne De Bellevue PQ H9X 3R2 Canada McGill Univ Dept Elect & Comp Engn Montreal PQ H3A 2A7 Canada

Automatically optimizing the design of a microwave device can be prohibitively time-consuming when a numerical electromagnetic-field analysis is necessary at each iteration. However, the time taken for the field analysis depends on the accuracy required, and in the early stage of the optimization relatively inaccurate solutions are adequate. This idea is exploited in a scheme that combines a quasi-Newton constrained optimizer with a two-dimensional p-adaptive finite-element method for finding scattering parameters. The scheme has been tested on three H-plane rectangular waveguide devices: a T-junction, a miter bend with a dielectric column, and a two-cavity iris-coupled filter. Time savings of more than an order of magnitude were obtained, compared to the standard approach of requiring equally high accuracy throughout the optimization.

关键词： design automation electromagnetic scattering finite-element methods microwave devices optimization methods

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kFEM: Adaptive meshfree finite-element methods using local kernels on arbitrary subdomains

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INTERNATIONAL JOURNAL FOR NUMERICAL methods IN ENGINEERING 2018年第6期114卷 581-597页

作者： Quaglino, A. Krause, R. Univ Svizzera Italiana Inst Computat Sci CH-6900 Lugano Switzerland

We propose a novel finite-element method for polygonal meshes. The resulting scheme is hp-adaptive, where h and p are a measure of, respectively, the size and the number of degrees of freedom of each polygon. Moreover, it is locally meshfree, since it is possible to arbitrarily choose the locations of the degrees of freedom inside each polygon. Our construction is based on nodal kernel functions, whose support consists of all polygons that contain a given node. This ensures a significantly higher sparsity compared to standard meshfree approximations. In this work, we choose axis-aligned quadrilaterals as polygonal primitives and maximum entropy approximants as kernels. However, any other convex approximation scheme and convex polygons can be employed. We study the optimal placement of nodes for regular elements, ie, those that are not intersected by the boundary, and propose a method to generate a suitable mesh. Finally, we show via numerical experiments that the proposed approach provides good accuracy without undermining the sparsity of the resulting matrices.

关键词： adaptivity elasticity finite-element methods meshfree methods

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Time-domain finite-element methods

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 1997年第3期45卷 430-442页

作者： Lee, JF Lee, R Cangellaris, A OHIO STATE UNIV DEPT ELECT ENGNELECTROSCI LABCOLUMBUSOH 43210 UNIV ARIZONA DEPT ELECT & COMP ENGNELECTROMAGNET LABTUCSONAZ 85721

In this paper, various time-domain finite-element methods for the simulation of transient electromagnetic wave phenomena are discussed, Detailed descriptions of test/trial spaces, explicit and implicit formulations, nodal and edge/facet element basis functions are given, along with the numerical stability properties of the different methods, The advantages and disadvantages of mass lumping are examined, Finally, the various formulations are compared on the basis of their numerical dispersion performance.

关键词： electromagnetic transient analysis finite-element methods

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Perfectly matched layer mesh terminations for nodal-based finite-element methods in electromagnetic scattering

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 1998年第4期46卷 507-516页

作者： Tang, JW Paulsen, KD Haider, SA Dartmouth Coll Thayer Sch Engn Hanover NH 03755 USA

The perfectly matched layer (PML) concept introduced by Berenger is implemented for nodal-based finite-element frequency-domain methods. Starting from a scalar/vector potential framework, anisotropic media-equivalent gauge conditions are developed for both coupled and uncoupled (i.e., direct field) scalar/vector field formulations. The resulting discrete system of equations are shown to be identical for both the anisotropic and stretched coordinate viewpoints of PML mesh termination on node-based finite elements, Reaching this equivalency requires that special attention be paid to the basis/weighting functions used within the PML region, specifically, a material dependency is found to be essential. The alternative but identical stretched coordinate approach provides the perspective needed to realize a scheme for generalizing the PML to non-Cartesian mesh terminations which are more natural in the finite-element context, Several benchmark problems and associated numerical results are presented to demonstrate the performance of the PML on node-based finite elements.

关键词： electromagnetic scattering finite-element methods perfectly matched layer

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Regularity constants of the Stokes problem.: Application to finite-element methods on curved domains

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MATHEMATICAL MODELS & methods IN APPLIED SCIENCES 2005年第3期15卷 437-470页

作者： Ayuso, B García-Archilla, B Univ Autonoma Madrid Dept Matemat E-28049 Madrid Spain Univ Seville Escuela Super Ingn Dept Matemat Aplicada 2 Seville 41092 Spain

For bounded smooth domains, we study how the solution of the Stokes problem is bounded in terms of the data when the domain changes. We show that standard bounds for a fixed domain hold with the same constant for wide classes of domains. This is done by first reviewing the original results of Cattabriga and then, in terms of geometric properties of the domains, by specifying when to apply Cattabriga's intermediate results. We do the same with standard strong extension and trace theorems. We apply these results to an elegant technique of analysis due to Wahlbin to overcome the disparity between a curved domain and the domains where finite-element computations are carried out in practice without resorting to numerical quadrature.

关键词： regularity Stokes problem finite-element methods curved domains

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