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Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method
2016
Computer Methods in Applied Mechanics and Engineering
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The linear complexity is achieved by transforming the dense system into an extended sparse system, along with the compression of certain matrix blocks into low-rank factorizations. ...
Numerical benchmarks are presented, demonstrating that the proposed approach enhances the computational efficiency of mesh deformation algorithms based on radial basis function interpolation significantly ...
Acknowledgments The authors would like to thank Heather Kline and Thomas Economon at Stanford University for their assistance in obtaining the results presented in Section 5. ...
doi:10.1016/j.cma.2016.05.029
fatcat:e26hfcxgwzbejk2a32m5ws43ey
Shape optimization for the strong directional scattering of dielectric nanorods
2021
International Journal for Numerical Methods in Engineering
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Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. ...
Specifically, the so-called light routing has application in photovoltaics, on-chip light routing for integrated optical circuits, field-enhanced and surface-enhanced spectroscopy, ultracompact nanoantennas ...
This work was supported by the Kempe foundation under Grant No. SMK-1857 and the Swedish strategic research programme eSSENCE. ...
doi:10.1002/nme.6677
fatcat:af4do3fp7radtpwq7np7gbhwai
An iterative hyperelastic parameters reconstruction for breast cancer assessment
2008
Medical Imaging 2008: Physiology, Function, and Structure from Medical Images
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Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue. ...
The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. ...
The phantom's FE mesh was constructed using a transfinite interpolation meshing technique. ...
doi:10.1117/12.770971
fatcat:alwlxb4x4nex3ovy455ld7bsnm
High order transition elements: The xNy-element concept – Part I: Statics
[article]
2019
arXiv
pre-print
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The approach is based on the transfinite mapping concept and constitutes an extension/generalization of the pNh-element concept. ...
By means of several numerical examples, the convergence behavior is investigated in detail, and the asymptotic rates of convergence are determined numerically. ...
In this framework, the term transfinite means that the interpolation of an arbitrary function matches the original function at a non-denumerable (transfinite 5 ) set of points [34] , i.e., the functions ...
arXiv:1909.04899v2
fatcat:p2bj7tpfkzdh5c5r2etatzl53u
Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points
2011
Mathematics of Computation
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Using the concept of Geometric Weakly Admissible Meshes (see §2 below) together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate ...
least squares approximation and Lagrange interpolation. ...
In Table 2 we compare, for the two test functions below, the errors (in the uniform norm) of discrete least squares approximation on the AM and on the WAM of the disk, and of interpolation at the Approximate ...
doi:10.1090/s0025-5718-2011-02442-7
fatcat:nnfy2cqazjcplb4quhwnykjzuu
Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points
[article]
2009
arXiv
pre-print
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Using the concept of Geometric Weakly Admissible Meshes together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares ...
approximation and Lagrange interpolation. ...
In Table 3 we compare, for the three test functions below, the errors (in the uniform norm) of discrete least squares approximation on the AM and on the WAM of the disk, and of interpolation at the Approximate ...
arXiv:0902.0215v1
fatcat:gwnj5vz5ljbstajttgnqidovsi
G1 interpolation using piecewise quadric and cubic surfaces
1990
Curves and Surfaces in Computer Vision and Graphics
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A combination of techniques are used from computational algebraic geometry and numerical approximation theory which reduces the problem to solving coupled systems of linear equations and low degree, polynomial ...
In this paper, we focus on the use of low degree, implicitly defined, algebraic surfaces in three dimensional real space IR.3. ...
Other approaches to parametric surface fitting and transfinite interpolation are also mentioned in that paper, as well as in [24] . ...
doi:10.1117/12.19736
fatcat:64kdqd4m65gfjorjr7m7ltv3ye
An iterative domain decomposition, spectral finite element method on non-conforming meshes suitable for high frequency Helmholtz problems
[article]
2018
arXiv
pre-print
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By increasing the size of the coarse space according to this criterion, the number of iterations in the domain decomposition method depends only weakly on the wavenumber. ...
We demonstrate this convergence behaviour on standard domain decomposition test problems and conclude the paper with application of the method to electromagnetic problems in two dimensions. ...
Acknowledgments We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number 121777]. ...
arXiv:1808.04713v1
fatcat:xsdjbinzefan5lwvmpcpbec3hy
Generalized sweep templates for implicit modeling
2005
Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia - GRAPHITE '05
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Flat endcaps are introduced into the 3D sweep formulation, which is implemented in the context of an interactive hierarchical implicit volume modeling tool. ...
A technique is presented for generating implicit sweep objects that support direct specification and manipulation of the surface with no topological limitations on the 2D sweep template. ...
Acknowledgements The authors would like to thank the reviewers for their valuable comments. This work was supported by the National Science and Engineering Research Council of Canada and iCore. ...
doi:10.1145/1101389.1101428
dblp:conf/graphite/SchmidtW05
fatcat:6tybv4d3wrewfkbrulzcwargpy
An effective high order interpolation scheme in BIEM for biharmonic boundary value problems
2005
Engineering analysis with boundary elements
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All boundary values including geometries are approximated by high order radial basis function networks (RBFNs) rather than the conventional low order Lagrange interpolation schemes. ...
For a better quality of approximation, the networks representing the boundary values and their derivatives are constructed by using integration processes. ...
Mai-Duy wishes to thank the University of Sydney for a Sesqui Postdoctoral Research Fellowship. We would like to thank the referees for their helpful comments. ...
doi:10.1016/j.enganabound.2005.01.005
fatcat:b5lefrkq6ngcdgq5ku6yzuocum
Comparison of Gradient-Based and Gradient-Enhanced Response-Surface-Based Optimizers
2010
AIAA Journal
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Acknowledgments The computer implementation of J. Burkardt (http://www.scs.fsu.edu/ ~burkardt/) was used to generate the initial space filling sampling and the genetic algorithm of D. ...
Caroll was used for optimization on response surfaces. Authors would like to thank them for sharing their work. Authors also thank H. Moet for helping them correct this paper. ...
Once computed, the field of deformation on the surface skin is spread in the volume mesh using a mixed integral / transfinite interpolation method. ...
doi:10.2514/1.45331
fatcat:el7ezlndcng6pl2bhii2ghfp4q
Rigorous body-order approximations of an electronic structure potential energy landscape
[article]
2021
arXiv
pre-print
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Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature ...
We discuss potential consequences of this observation for modelling the potential energy landscape, as well as for solving the electronic structure problem. ...
rate and the errors in the approximation based on interpolation. ...
arXiv:2106.12572v1
fatcat:b5orlz7oxzcuhospxfx37jxs5e
Limits and C*-algebras of low rank or dimension
[article]
2007
arXiv
pre-print
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We identify some conditions under which the constructions preserve low rank for the C*-algebras or their multiplier algebras. ...
We explore various limit constructions for C*-algebras, such as composition series and inverse limits, in relation to the notions of real rank, stable rank, and extremal richness. ...
By [4] , see also the explanatory version in [10] , there is an interpolating projection q in M (I) such that if f ± are (any) two continuous functions vanishing on [−1, 1 2 ] and [− 1 2 , 1] , respectively ...
arXiv:0708.2727v1
fatcat:onybvkfilbeibl7zub24mso4km
Author Index Volume 233 (2010)
2010
Journal of Computational and Applied Mathematics
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Floater, Transfinite mean value interpolation in general dimension 1631-1639 Bultheel, A., P. Van gucht and M. Van Barel, Bunse-Gerstner, A., D. Kubalińska, G. Vossen and D. Cambini, R. and F. ...
Salvi, A branch and reduce approach for solving a class of low rank d.c. programs 492-501 Campbell, S.L. and P. Kunkel, Completions of Ceng, L.C., D.R. Sahu and J.C. ...
doi:10.1016/s0377-0427(10)00093-2
fatcat:xlsind2vobapvhbyhuof55lyhe
Multi-Index Stochastic Collocation for random PDEs
2016
Computer Methods in Applied Mechanics and Engineering
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We then provide a complexity analysis that assumes decay rates of product type for such mixed differences, showing that in the optimal case the convergence rate of MISC is only dictated by the convergence ...
of the deterministic solver applied to a one dimensional problem. ...
[6, 7, 8, 9] ), low-rank techniques [10, 11, 12, 13] and reduced basis methods (see e.g. [14, 15] ). ...
doi:10.1016/j.cma.2016.03.029
fatcat:au6mybcvfraa3ig3gi4cfsl3ou
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