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A sparse-grid isogeometric solver

Joakim Beck, Giancarlo Sangalli, Lorenzo Tamellini
2018 Computer Methods in Applied Mechanics and Engineering  
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]

Pablo Antolin and Annalisa Buffa and Emiliano Cirillo
2021 arXiv   pre-print
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

A. Abbadi, D. Barrera, M.J. Ibáñez, D. Sbibih
2010 Journal of Computational and Applied Mathematics  
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/ fatcat:ubaxne7t6raw3bu47snbrrd4ma

Field-aligned online surface reconstruction

Nico Schertler, Marco Tarini, Wenzel Jakob, Misha Kazhdan, Stefan Gumhold, Daniele Panozzo
2017 ACM Transactions on Graphics  
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]

Chantal Racette
2012 arXiv   pre-print
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  
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

Robert Schaback, Holger Wendland
2006 Acta Numerica  
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)

Alin Anton, Ioan Cretu
2011 Zenodo  
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

Dominik Błoński, Katarzyna Strzelecka, Henryk Kudela
2021 Energies  
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]

Marcel Campen
2017 Eurographics State of the Art Reports  
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

B. Gilles, L. Revéret, D. K. Pai
2010 Computer graphics forum (Print)  
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

G. Andrés Cisneros, Mikko Karttunen, Pengyu Ren, Celeste Sagui
2013 Chemical Reviews  
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

Gerhard H. Bendels, Ruwen Schnabel, Reinhard Klein
2006 Journal of WSCG  
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 (  ... 
dblp:journals/jwscg/BendelsSK06 fatcat:w5s6pqx5sreffjnrxg7dz43nda

Optimal nonlinear approximation

Ronald A. DeVore, Ralph Howard, Charles Micchelli
1989 Manuscripta mathematica  
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

Ronald A. DeVore
1998 Acta Numerica  
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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