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A hierarchical construction of LR meshes in 2D

Andrea Bressan, Bert Jüttler
2015 Computer Aided Geometric Design  
In contrast to the original LRpaper (Dokken et al., 2013) and similarly to the hierarchical B-spline framework (Forsey and Bartels, 1988 ) the construction of the mesh is based on a priori choice of a  ...  We describe a construction of LR-spaces whose bases are composed of locally linearly independent B-splines which also form a partition of unity.  ...  Michael Pauley for commenting on an earlier version of this paper.  ... 
doi:10.1016/j.cagd.2015.06.002 fatcat:gofjwhcsjfg5xko3oyqmtfqw7i

On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines

Kjetil André Johannessen, Filippo Remonato, Trond Kvamsdal
2015 Computer Methods in Applied Mechanics and Engineering  
is not covered by LR B-splines and it is thus not possible to construct a basis on the same mesh and do a comparison study.  ...  We will look at how an admissible mesh is constructed, and how the construction procedure defines a sequence of nested bounded domains linked to the different Hierarchical levels. 3.2.1 Introduction  ... 
doi:10.1016/j.cma.2015.02.031 fatcat:i3cdktv3dvfibgcdtf4fh4g5hm

LR B-Splines implementation in the Altair RadiossTM solver for explicit dynamics IsoGeometric Analysis

M. Occelli, T. Elguedj, S. Bouabdallah, L. Morançay
2019 Advances in Engineering Software  
To this end, the necessary ingredients to a smooth integration of IGA in a traditional finite element code have been identified and adapted to the existing code architecture.  ...  A challenging task is still to move IGA from a proof of concept to a convenient design tool for industry and this work contributes to this endeavor.  ...  LR B-Splines in 3D and overloaded elements LR B-Spline refinement is constructed in 1D by inserting one singular knot or a mesh line in 2D.  ... 
doi:10.1016/j.advengsoft.2019.01.002 fatcat:myktdsp34bfkffthzjpqd2jnqi

A Versatile Strategy for the Implementation of Adaptive Splines [chapter]

Andrea Bressan, Dominik Mokriš
2017 Lecture Notes in Computer Science  
nested refinement and hierarchical LR-splines.  ...  This paper presents an implementation framework for spline spaces over T-meshes (and their d-dimensional analogs). The aim is to share code between the implementation of several spline spaces.  ...  Acknowledgments The authors have been supported by the Austrian Science Fund (FWF, NFN S117 "Geometry + Simulation") and by the Seventh Framework Programme of the EU (project EXAMPLE, GA No. 324340).  ... 
doi:10.1007/978-3-319-67885-6_3 fatcat:4cb4ai2ttbaqffcmg7c6adkqd4

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes [article]

Francesco Patrizi, Tor Dokken
2019 arXiv   pre-print
In this paper we address the minimal number of B-splines that can form a linear dependence relation for Minimal Support B-splines (MS B-splines) and for Locally Refinable B-splines (LR B-splines) on LR-meshes  ...  The focus on locally refined spline spaces has grown rapidly in recent years due to the need in Isogeoemtric analysis (IgA) of spline spaces with local adaptivity: a property not offered by the strict  ...  Spline space over a box-mesh in 1D and 2D In this section we define the spline spaces over box-meshes in 1D and 2D and present the dimension formulas of them.  ... 
arXiv:1811.04919v2 fatcat:rwkgh5lrw5cnfb7cad6utse4aa

Modified T-splines

Hongmei Kang, Falai Chen, Jiansong Deng
2013 Computer Aided Geometric Design  
The basic idea is to construct a set of basis functions for a given T-mesh that have the following nice properties: non-negativity, linear independence, partition of unity and compact support.  ...  T-splines are a generalization of NURBS surfaces, the control meshes of which allow Tjunctions.  ...  The work is supported by 973 Program 2011CB302400, the NSF of China No. 11031007.  ... 
doi:10.1016/j.cagd.2013.09.001 fatcat:xhbhmxhmr5bkhizyffwtgind2m

THB-splines: An effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis

Carlotta Giannelli, Bert Jüttler, Stefan K. Kleiss, Angelos Mantzaflaris, Bernd Simeon, Jaka Špeh
2016 Computer Methods in Applied Mechanics and Engineering  
The use of hierarchical constructions in isogeometric analysis is a very promising approach [14, 38, 43] .  ...  Polynomial splines over hierarchical T-meshes [30] are based on a different paradigm to construct bases for the entire space of piecewise polynomials with a given smoothness on a certain subdivision of  ...  Anh-Vu Vuong for collaborating with us at an earlier stage of this research.  ... 
doi:10.1016/j.cma.2015.11.002 fatcat:saqayplxhfhxnjwnw74peza2bu

Scaling towards kilo-core processors with asymmetric high-radix topologies

N. Abeyratne, R. Das, Qingkun Li, K. Sewell, B. Giridhar, R. G. Dreslinski, D. Blaauw, T. Mudge
2013 2013 IEEE 19th International Symposium on High Performance Computer Architecture (HPCA)  
By setting a design goal of matching router speed with wire speed, our proposed topologies use fast medium-radix routers to optimize for local communication and a few slow high-radix routers that reduce  ...  Our evaluations show that the best performing asymmetric high-radix topology improves average network latency over a mesh by 45% while reducing the power consumption by 40%.  ...  We thank the generous support of our industrial sponsor, ARM Ltd.  ... 
doi:10.1109/hpca.2013.6522344 dblp:conf/hpca/AbeyratneDLSGDBM13 fatcat:azgwgm33qffgnekwnmqcgk264m

Post-processing and visualization techniques for isogeometric analysis results

Annette Stahl, Trond Kvamsdal, Christian Schellewald
2017 Computer Methods in Applied Mechanics and Engineering  
Isogeometric Analysis (IGA) introduced in 2005 by Hughes et al. (2005) [1] exploits one mathematical basis representation for computer aided design (CAD), geometry and analysis during the entire engineering  ...  In this paper we extend this concept also for visualization. The presented post-processing and visualization techniques thereby strengthen the relation between geometry, analysis and visualization.  ...  They also acknowledge the support from the other co-workers in the ICADA-project.  ... 
doi:10.1016/j.cma.2016.10.040 fatcat:if2uyoutlzhuxislqse2ujzvsy

Multi-feature super-resolution network for cloth wrinkle synthesis [article]

Lan Chen, Xiaopeng Zhang, Juntao Ye
2020 arXiv   pre-print
Each simulated mesh pair are then converted into a pair of low and high resolution "images" (a 2D array of samples), with each sample can be interpreted as any of three features: the displacement, the  ...  In this paper we propose a deep learning based method for synthesizing cloth animation with high resolution meshes.  ...  In addition to simulating The training for each model takes about a day and a half on a a piece of tablecloth in a free environment, we also construct a GeForce R GTX 1080Ti of  ... 
arXiv:2004.04351v1 fatcat:v3fnxtdtpbdlxmpejndslu7ghu

Adaptive local surface refinement based on LR NURBS and its application to contact

Christopher Zimmermann, Roger A. Sauer
2017 Computational Mechanics  
An automatic remeshing technique is presented that allows adaptive local refinement and coarsening of LR NURBS. In this work, LR NURBS are applied to contact computations of 3D solids and membranes.  ...  The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis.  ...  LR B-splines have been successfully used in 2D, since they are linearly independent in 2D. In 3D, the linear independence does not seem to exist for arbitrary, locally refined meshes.  ... 
doi:10.1007/s00466-017-1455-7 fatcat:b3dkxfr6ujg43lk3iao35lqqum

Adaptive Extended Isogeometric Analysis for Steady-State Heat Transfer in Heterogeneous Media

Weihua Fang, Tiantang Yu, Yin Yang
2021 CMES - Computer Modeling in Engineering & Sciences  
In the XIGA, the LR NURBS, which have a simple local refinement algorithm and good description ability for complex geometries, are employed to represent the geometry and discretize the field variables;  ...  (LR NURBS).  ...  Acknowledgement: The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper.  ... 
doi:10.32604/cmes.2021.014575 fatcat:osynjd4jz5ef7d46ipcwai2qpy

A fast block low-rank dense solver with applications to finite-element matrices

AmirHossein Aminfar, Sivaram Ambikasaran, Eric Darve
2016 Journal of Computational Physics  
of their corresponding vertices in the sparse matrix graph.  ...  To construct the low-rank approximation of the off-diagonal blocks, we propose a new pseudo-skeleton scheme, the boundary distance low-rank approximation, that picks rows and columns based on the location  ...  Matrix Mesh Level Matrix Size LR 1e-1 1e-3 1e-5 LU Speed Type Type Sparse Dense Method LR P T I LR P T I LR P T I Table 4 : Summary of solver speed for various benchmark cases  ... 
doi:10.1016/j.jcp.2015.10.012 fatcat:whfyef23erhjnpyiox4bhfrzdm

Hierarchical interconnection networks for multicomputer systems

S.P. Dandamudi, D.L. Eager
1990 IEEE transactions on computers  
a large number of processors are to be connected, for the reasons described in Section 11-A.  ...  A performance analysis of a class of hierarchical interconnection networks is presented. This analysis includes both static analysis (i.e., queueing delays are neglected) and queueing ana1ysis.  ...  Carlson [4] proposes a two-level mesh hierarchy scheme: the mesh with a global mesh structure.  ... 
doi:10.1109/12.53600 fatcat:sam37pvpdjhuvpugwtbvjttx6a

Adaptively Merging Large-Scale Range Data with Reflectance Properties [chapter]

Ryusuke Sagawa, Ko Nishino, Katsushi Ikeuchi
2008 Digitally Archiving Cultural Objects  
We construct an integrated mesh model of the target object in adaptive resolution, taking into account the geometric and/or photometric attributes associated with the range images.  ...  This adaptive merging framework leads to a significant reduction in the necessary amount of computational resources.  ...  Since a transformed cube becomes a skewed rectangle or a triangle in a 2D slice of the volume, as shown in Fig. 5 , the vertices of the mesh model generated by MC are on those edges.  ... 
doi:10.1007/978-0-387-75807_10 fatcat:3qtiqstzy5arvnsizgoo74gqwq
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