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A sparse-grid isogeometric solver
2018
Computer Methods in Applied Mechanics and Engineering
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Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. ...
meshes. ...
The meshes of the three components of f J=1 in (13) are the three leftmost meshes, while the right-most mesh is the one of the full tensor grid approximation f [1, 1] . ...
doi:10.1016/j.cma.2018.02.017
fatcat:ffpc2phtlref5lzt5rhdutxaim
Region extraction in mesh intersection
[article]
2021
arXiv
pre-print
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Most of the literature focuses on regions delimited by straight lines, often in the special case of intersection detection among two unstructured meshes. ...
While classical region extraction algorithms for line drawings and mesh intersection algorithms have proved to be able to deal with many applications, the advances in Isogeometric Analysis require a generalization ...
Lee and colleagues proposed Segments based integration schemes are based on the
an algorithm based on the construction of a background approximation of the ...
arXiv:2112.03181v1
fatcat:3stovbpzd5fwxkupnoqppf7mf4
A general method for constructing quasi-interpolants from B-splines
2010
Journal of Computational and Applied Mathematics
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A general method for constructing quasi-interpolation operators based on B-splines is developed. ...
Given a B-spline φ in R s , s ≥ 1, normalized by i∈Z s φ (· − i) = 1, the classical structure Q (f ) := i∈Z s λf (· + i) φ (· − i), for a quasi-interpolation operator Q is considered. ...
Acknowledgements We would like to thank the anonymous referees for pertinent comments which helped us to improve this paper. ...
doi:10.1016/j.cam.2010.01.017
fatcat:ubaxne7t6raw3bu47snbrrd4ma
Field-aligned online surface reconstruction
2017
ACM Transactions on Graphics
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editing tools with immediate visual feedback on the output mesh. ...
realized using only weak notions of spatial neighborhoods, which allows for an implementation that scales approximately linearly with the size of each dataset that is integrated into a partial reconstruction ...
The orientations satisfy a rotational symmetry (RoSy) condition, such that each direction is part of an equivalence class with three other elements (grey arrows); a hierarchical optimization scheme optimizes ...
doi:10.1145/3072959.3073635
fatcat:btht7sueavafvn5vqvq35ye45y
Numerical Analysis of Diagonal-Preserving, Ripple-Minimizing and Low-Pass Image Resampling Methods
[article]
2012
arXiv
pre-print
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Methods tuned for natural image upsampling (roughly speaking, image enlargement) are analyzed and developed with a focus on their ability to preserve diagonal features and suppress overshoots. ...
for relative error minimization in the presence of roots in the interior of the interval of approximation and so that even and odd functions are approximated with like polynomials. ...
, and then applying a one-dimensional scheme in the vertical direction to the result (or vice versa). ...
arXiv:1204.4734v1
fatcat:p6zo3ddp5vbavkawnh45oknpti
Overview of Volume Rendering
[chapter]
2005
Visualization Handbook
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A second-order interpolation filter that yields a f(x,y,z) with a continuous first derivative is the cardinal spline function, whose 1D function is given by (see blue curve in Fig. 4 ): (5) Here, u ...
In the former case, three texture stacks are needed, one for each major viewing direction. ...
doi:10.1016/b978-012387582-2/50009-5
fatcat:gthzcwcaanhuvhpmab7ii6r5fa
Kernel techniques: From machine learning to meshless methods
2006
Acta Numerica
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It uncovers the links between them, as far as they are related to kernel techniques. It addresses non-expert readers and focuses on practical guidelines for using kernels in applications. ...
Kernels are valuable tools in various fields of Numerical Analysis, including approximation, interpolation, meshless methods for solving partial differential equations, neural networks, and Machine Learning ...
To derive a similar result for the general moving least squares approximation scheme, it is important to rewrite the approximant in form of a quasi-interpolant s f,X (x) = N j=1 u m j (x)f (x j ) like ...
doi:10.1017/s0962492906270016
fatcat:hmwsgedodbfujlh6qusweugsyu
Space-Time Window Reconstruction In Parallel High Performance Numeric Simulations. Application For Cfd (Phd Thesis)
2011
Zenodo
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This thesis proposes a new concept for dealing with large-scale, numerical simulation data. ...
Supercomputing today is like riding a barouche with horses that travel orders of magnitude faster than the storage; long distance runs, add hills, and valleys, to the landscape; high performance computing ...
Tetrahedral interpolation is used for the initial 3D fields, and it works well on unstructured meshes with higher-order polyhedrons; however, the results may be different depending on the way a particular ...
doi:10.5281/zenodo.15938
fatcat:xh4i6ig7qvfkjapq76phiadpje
Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation
2021
Energies
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The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. ...
A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. ...
The process of redistribution of the particle mass was done by a Z 2 cardinal splines interpolation kernel, that conserves the moment of vortex particle up to the 2nd degree (zero-quantity of vorticity ...
doi:10.3390/en14248402
fatcat:5mopr2n2vjdsbmmxky6mq7wjyq
Partitioning Surfaces into Quad Patches
[article]
2017
Eurographics State of the Art Reports
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Research in geometry processing has led to a variety of automatic or semi-automatic approaches to address this problem. ...
the use of tensor-product representations based on NURBS or Bézier patches, grid-based multiresolution techniques, or discrete pixel-based map representations. ...
Bézier triangles and certain types of box splines are examples of such representations. ...
doi:10.2312/egt.20171033
fatcat:kjobkceodfftfhw4l7ttaya4qm
Creating and Animating Subject-Specific Anatomical Models
2010
Computer graphics forum (Print)
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of the template, while global and discontinuous displacements are estimated through a projection onto a statistical shape model and a new joint pose optimization scheme with joint limits. ...
This allows for noise reduction, bone separation, and the transfer, from the template, of anatomical and kinematical information not present in the input data. ...
We would like to thank Olivier Palombi, Jean-Francois Le bas and Irene Tropres from the Grenoble hospital for MRI acquisition. ...
doi:10.1111/j.1467-8659.2010.01718.x
fatcat:3j3zcdkyizeb5jqqs23nujakkq
Classical Electrostatics for Biomolecular Simulations
2013
Chemical Reviews
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G.A.C. thanks Wayne State University, M.K. thanks the Natural Sciences and Engineering Research Council of Canada, P.R. thanks the Robert A. ...
Duke for sharing with us his experience with truncation methods. We would like to thank the support we have received for this work. ...
The method approximates the complex exponentials in the reciprocal sum by an Euler spline interpolation, based on cardinal B-splines in the smooth PME. 44 B-splines are factored into three one-dimensional ...
doi:10.1021/cr300461d
pmid:23981057
pmcid:PMC3947274
fatcat:436zql6ojzgnbhd2q3hs7x5fhq
Detecting Holes in Point Set Surfaces
2006
Journal of WSCG
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An international journal of algorithms, data structures and techniques for computer graphics and visualization, surface meshing and modeling, global illumination, computer vision, image processing and ...
ACKNOWLEDGEMENTS The authors would like to thank Udo Tremel from EADS Military Aircraft for the beautiful F16-like simulation data, and Uli Bieg from the University of Tübingen for the mesh of the Burdigalian ...
ACKNOWLEDGMENTS The research is a part of the basic research on visualization conducted in cooperation between the Comenius University, Bratislava and the VRVis Research Center in Vienna (http://www.vrvis.at ...
dblp:journals/jwscg/BendelsSK06
fatcat:w5s6pqx5sreffjnrxg7dz43nda
Optimal nonlinear approximation
1989
Manuscripta mathematica
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Acknowledgements The author thanks Professors de Boor, Cohen, Oskolkov, Petrushev and Temlyakov for their valuable suggestions concerning this survey. ...
These are difficult problems and have to a large extent been abandoned with the advent of box splines and, later, wavelets. ...
In the process, we shall engage three types of spaces: approximation spaces, interpolation spaces, and smoothness spaces. ...
doi:10.1007/bf01171759
fatcat:navvf36rxvfvtiytuiz6wwb2ju
Nonlinear approximation
1998
Acta Numerica
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Acknowledgements The author thanks Professors de Boor, Cohen, Oskolkov, Petrushev and Temlyakov for their valuable suggestions concerning this survey. ...
These are difficult problems and have to a large extent been abandoned with the advent of box splines and, later, wavelets. ...
In the process, we shall engage three types of spaces: approximation spaces, interpolation spaces, and smoothness spaces. ...
doi:10.1017/s0962492900002816
fatcat:sesusbobb5gmdggsklxk4z72uq
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