399 research outputs found
Implicit Density Functional Theory
A fermion ground state energy functional is set up in terms of particle
density, relative pair density, and kinetic energy tensor density. It satisfies
a minimum principle if constrained by a complete set of compatibility
conditions. A partial set, which thereby results in a lower bound energy under
minimization, is obtained from the solution of model systems, as well as a
small number of exact sum rules. Prototypical application is made to several
one-dimensional spinless non-interacting models. The effectiveness of "atomic"
constraints on model "molecules" is observed, as well as the structure of
systems with only finitely many bound states.Comment: 9 pages, 4 figure
The Influence of Quadrature Errors on Isogeometric Mortar Methods
Mortar methods have recently been shown to be well suited for isogeometric
analysis. We review the recent mathematical analysis and then investigate the
variational crime introduced by quadrature formulas for the coupling integrals.
Motivated by finite element observations, we consider a quadrature rule purely
based on the slave mesh as well as a method using quadrature rules based on the
slave mesh and on the master mesh, resulting in a non-symmetric saddle point
problem. While in the first case reduced convergence rates can be observed, in
the second case the influence of the variational crime is less significant
Extended isogeometric analysis for cohesive fracture
The objective of this study is to present an extended isogeometric formulation for cohesive fracture. The approach exploits the higher order interelement continuity property of nonuniform rational Bâsplines (NURBS), in particular the higher accuracy that results for the stress prediction, which yields an improved estimate for the direction of crack propagation compared to customary Lagrangian interpolations. Shifting is used to ensure compatibility with the surrounding discretization, where, different from extended finite element methods, the affected elements stretch over several rows perpendicular to the crack path. To avoid fine meshes around the crack tip in case of cohesive fracture, a blending function is used in the extension direction of the crack path. To comply with standard finite element data structures, BĂ©zier extraction is used. The absence of the Kroneckerâdelta property in the higher order interpolations of isogeometric analysis impedes the enrichment scheme and compatibility enforcement. These issues are studied comprehensively at the hand of several examples, while crack propagation analyses show the viability of the approach
Building information modelling â A novel parametric modeling approach based on 3D surveys of historic architecture
Building Information Modelling (BIM) appears to be the best answer to simplify the traditional process of design, construction, management and maintenance. On the other hand, the intricate reality of the built heritage and the growing need to represent the actual geometry using 3D models collide with the new paradigms of complexity and accuracy, opening a novel operative perspective for restoration and conservation. The management of complexity through BIM requires a new management approach focused on the development of improve the environmental impact cost, reduction and increase in productivity and efficiency the Architecture, Engineering and Construction (AEC) Industry. This structure is quantifiable in morphological and typical terms by establishing levels of development and detail (LoDs) and changes of direction (ReversLoDs) to support the different stages of life cycle (LCM). Starting from different experiences in the field of HBIM, this research work proposes a dynamic parametric modeling approach that involves the use of laser scanning, photogrammetric data and advanced modelling for HBIM
A B-Spline-Based Generative Adversarial Network Model for Fast Interactive Airfoil Aerodynamic Optimization
Airfoil aerodynamic optimization is of great importance in aircraft design; however, it relies on high-fidelity physics-based models that are computationally expensive to evaluate. In this work, we provide a methodology to reduce the computational cost for airfoil aerodynamic optimization. Firstly, we develop a B-spline based generative adversarial networks (BSplineGAN) parameterization method to automatically infer design space with sufficient shape variability. Secondly, we construct multi-layer neural network (MNN) surrogates for fast predictions on aerodynamic drag, lift, and pitching moment coefficients. The BSplineGAN has a relative error lower than 1% when fitting to UIUC database. Verification of MNN surrogates shows the root means square errors (RMSE) of all aerodynamic coefficients are within the range of 20%â40% standard deviation of testing points. Both normalized RMSE and relative errors are controlled within 1%. The proposed methodology is then demonstrated on an airfoil aerodynamic optimization. We also verified the baseline and optimized designs using a high-fidelity computational fluid dynamic solver. The proposed framework has the potential to enable web-based fast interactive airfoil aerodynamic optimization
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
Geometric characteristics of conics in BĂ©zier form
In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in BĂ©zier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the use of coordinates
Comparing faceted and smoothed tool surface descriptions in sheet metal forming simulation
This study deals with different tool surface description
methods used in the finite element analysis of sheet metal
forming processes. The description of arbitrarily-shaped tool
surfaces using the traditional linear finite elements is compared
with two distinct smooth surface description approaches:
(i) BĂ©zier patches obtained from the ComputerAided
Design model and (ii) smoothing the finite element
mesh using Nagata patches. The contact search algorithm is
presented for each approach, exploiting its special features in
order to ensure an accurate and efficient contact detection. The
influence of the tool modelling accuracy on the numerical
results is analysed using two sheet forming examples, the
unconstrained cylindrical bending and the reverse deep drawing
of a cylindrical cup. Smoothing the contact surfaces with
Nagata patches allows creating more accurate tool models,
both in terms of shape and normal vectors, when compared
with the conventional linear finite element mesh. The computational
efficiency is evaluated in this study through the total
number of increments and the required CPU time. The mesh
refinement in the faceted description approach is not effective
in terms of computational efficiency due to large discontinuities
in the normal vector field across facets, even when
adopting fine meshes.The authors gratefully acknowledge the financial
support of the Portuguese Foundation for Science and Technology (FCT)
via the projects PTDC/EME-TME/118420/2010 and PEst-C/EME/
UI0285/2013 and by FEDER funds through the program COMPETE â
Programa Operacional Factores de Competitividade, under the project
CENTRO-07-0224-FEDER-002001 (MT4MOBI). The first author is
also grateful to the FCT for the PhD grant SFRH/BD/69140/2010.info:eu-repo/semantics/publishedVersio
Scene Segmentation Driven by Deep Learning and Surface Fitting
This paper proposes a joint color and depth segmentation scheme exploiting together geometrical clues and a learning stage. The approach starts from an initial over-segmentation based on spectral clustering. The input data is also fed to a Convolutional Neural Network (CNN) thus producing a per-pixel descriptor vector for each scene sample. An iterative merging procedure is then used to recombine the segments into the regions corresponding to the various objects and surfaces. The proposed algorithm starts by considering all the adjacent segments and computing a similarity metric according to the CNN features. The couples of segments with higher similarity are considered for merging. Finally the algorithm uses a NURBS surface fitting scheme on the segments in order to understand if the selected couples correspond to a single surface. The comparison with state-of-the-art methods shows how the proposed method provides an accurate and reliable scene segmentation
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