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Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method

Pieter Coulier, Eric Darve
2016 Computer Methods in Applied Mechanics and Engineering  
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

Juan C. Araújo, Eddie Wadbro
2021 International Journal for Numerical Methods in Engineering  
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

Hatef Mehrabian, Abbas Samani, Xiaoping P. Hu, Anne V. Clough
2008 Medical Imaging 2008: Physiology, Function, and Structure from Medical Images  
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]

Sascha Duczek, Albert Artha Saputra, Hauke Gravenkamp
2019 arXiv   pre-print
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

L. Bos, J.-P. Calvi, N. Levenberg, A. Sommariva, M. Vianello
2011 Mathematics of Computation  
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]

Len Bos, Jean-Paul Calvi, Norm Levenberg, Alvise Sommariva, Marco Vianello
2009 arXiv   pre-print
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

Chandrajit L. Bajaj, Leonard A. Ferrari, Rui J. P. de Figueiredo
1990 Curves and Surfaces in Computer Vision and Graphics  
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]

Ryan Galagusz, Steve McFee
2018 arXiv   pre-print
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

Ryan Schmidt, Brian Wyvill
2005 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia - GRAPHITE '05  
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

N. Mai-Duy, R.I. Tanner
2005 Engineering analysis with boundary elements  
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

J. Laurenceau, M. Meaux, M. Montagnac, P. Sagaut
2010 AIAA Journal  
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]

Jack Thomas, Huajie Chen, Christoph Ortner
2021 arXiv   pre-print
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]

Lawrence G. Brown, Gert K. Pedersen
2007 arXiv   pre-print
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  
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

Abdul-Lateef Haji-Ali, Fabio Nobile, Lorenzo Tamellini, Raúl Tempone
2016 Computer Methods in Applied Mechanics and Engineering  
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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