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Analytic methods for geometric modeling via spherical decomposition

Morad Behandish, Horea T. Ilieş
2016 Computer-Aided Design  
Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution  ...  We propose a new paradigm for more efficient computation of analytic correlations that relies on a grid-free discretization of arbitrary shapes as countable unions of balls, in turn described as sublevel  ...  Conclusion Analytic methods for geometric modeling have shown great promise in formulating and solving important problems in terms of convolutions, typically implemented by uniform grid-based sampling  ... 
doi:10.1016/j.cad.2015.06.016 fatcat:52r25jhyprdbhp3ubg54l7buza

Validating the Characteristic Modes Solvers

Miloslav Capek, Vit Losenicky, Lukas Jelinek, Mats Gustafsson
2017 IEEE Transactions on Antennas and Propagation  
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions.  ...  A noticeable advantage is the independence on feeding models. Both theoretical and numerical aspects of characteristic mode decomposition are discussed and illustrated by examples.  ...  ACKNOWLEDGEMENT The authors would like to thank Vladimir Sedenka from BUT and Michal Masek from CTU in Prague for implementing the method of moments and characteristic modes solvers within the AToM package  ... 
doi:10.1109/tap.2017.2708094 fatcat:onwy2otzzbh77ejmnks4y3ubha

Geometric Perspectives on Fundamental Solutions in the Linearized Satellite Relative Motion Problem [article]

Ethan Burnett, Hanspeter Schaub
2021 arXiv   pre-print
The Keplerian assumption enables an analytic approach, leads to new geometric insights, and allows for comparison to prior linearized relative motion solutions.  ...  By identifying the analytic relationship between Lyapunov-Floquet transformations of the relative motion dynamics in different coordinate systems, new means are provided for rapid computation and exploration  ...  This result highlights the possibility of future analytic work for computing the modal decompositions.  ... 
arXiv:2108.09608v1 fatcat:jlwfam2sdfhj7glpqy7vj3svjm

A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling

D. R. Davies, J. H. Davies, P. C. Bollada, O. Hassan, K. Morgan, P. Nithiarasu
2013 Geoscientific Model Development Discussions  
A method for incorporating multi-resolution capabilities within pre-existing global 3-D spherical mantle convection codes is presented.  ...  The method, which we term "geometric multigrid refinement", is based upon the application of a multigrid solver on non-uniform, structured grids and allows for the incorporation of local high-resolution  ...  The TERRA development team, particularly John Baumgardner, Hans-Peter Bunge and Marcus Mohr, are acknowledged for extensive support, whilst Ian Merrick is thanked for help with visualisation.  ... 
doi:10.5194/gmdd-6-2249-2013 fatcat:2ty542vehrbt7cqf4jitjm4qzu

A regularization approach for solving Poisson's equation with singular charge sources and diffuse interfaces [article]

Siwen Wang, Arum Lee, Emil Alexov, Shan Zhao
2019 arXiv   pre-print
For a spherical domain with diffuse interface, the proposed regularization method is numerically validated and compared with a semi-analytical quasi-harmonic method.  ...  For a sharp interface between inhomogeneous media, singular charges could be analytically treated by fundamental solutions or regularization methods.  ...  For a simple spherical problem, the regularization method is validated by comparing with a semi-analytical method and conventional trilineary distribution method.  ... 
arXiv:1910.00425v1 fatcat:2wtnnvh7ffc6rcu4vaurgvp7p4

A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling

D. R. Davies, J. H. Davies, P. C. Bollada, O. Hassan, K. Morgan, P. Nithiarasu
2013 Geoscientific Model Development  
</strong> A method for incorporating multi-resolution capabilities within pre-existing global 3-D spherical mantle convection codes is presented.  ...  The method, which we term "geometric multigrid refinement", is based upon the application of a multigrid solver on non-uniform, structured grids and allows for the incorporation of local high-resolution  ...  The TERRA development team, particularly John Baumgardner, Hans-Peter Bunge and Marcus Mohr, are acknowledged for extensive support, whilst Ian Merrick is thanked for help with visualisation.  ... 
doi:10.5194/gmd-6-1095-2013 fatcat:ymozo3jtofhhpm5vahrtishmbi

Magnetic dipole radiation tailored by substrates: numerical investigation

D. L. Markovich, P. Ginzburg, A. K. Samusev, P. A. Belov, A. V. Zayats
2014 Optics Express  
While the response of individual dielectric or metal spherical particles can be described analytically via multipole decomposition in the Mie series, the influence of substrates, in many cases present  ...  Optical properties of nanoparticles were characterized via scattering cross-section spectra, electric field profiles, and induced electric and magnetic moments.  ...  FDTD method allows analyzing spectral responses via single simulation by adopting the Fourier decomposition method with subsequent normalization.  ... 
doi:10.1364/oe.22.010693 pmid:24921770 fatcat:ttgah5g3inf6lfst4khzxb6myy

Efficient Spherical Harmonics Representation of 3D Objects

Mohamed-Hamed Mousa, Raphaelle Chaine, Samir Akkouche, Eric Galin
2007 15th Pacific Conference on Computer Graphics and Applications (PG'07)  
In this paper, we present a new and efficient spherical harmonics decomposition for spherical functions defining 3D triangulated objects.  ...  techniques, and provides a better control over the precision error in contrast to the voxel-based methods.  ...  Table 1 summarizes the timing of the computation of the spherical harmonics decomposition for the models presented in this paper.  ... 
doi:10.1109/pg.2007.39 dblp:conf/pg/MousaCAG07 fatcat:rtnonan6obew7jbujxkzckpvzu

Method of Moments and T-matrix Hybrid [article]

Vit Losenicky, Lukas Jelinek, Miloslav Capek, Mats Gustafsson
2021 arXiv   pre-print
Method performance is tested on a spherical multi-layer model of the human head.  ...  Along with the hybrid method, an evaluation of the transition matrix of an arbitrarily shaped object is presented and the characteristic mode decomposition is performed, exhibiting fourfold numerical precision  ...  matrix Γ is analytical for a spherical multi-layer.  ... 
arXiv:2012.04303v2 fatcat:34ywvff36fg6najj47yjwwl3je

Page 2445 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
The design optimization prob- lem is solved via a sequence of linearized subproblems. The com- putational model developed is tested in example problems.  ...  Methods Engrg. 38 (1995), no. 12, 1951-1965. Summary: “This paper presents the development of a compu- tational model for the topology optimization problem, using a material!  ... 

Analytic example of a free energy functional

Christian Tutschka, Gerhard Kahl
2000 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
The required input, the properties of the uniform fluid, is taken from the analytic mean spherical solution for these two systems.  ...  For hard spheres we derive-via a bilinear decomposition of the direct correlation functions-a set of basis functions, which is the same as the one presented by Rosenfeld in his fundamental measure theory  ...  Here, the direct correlation functions are known analytically for both the PY equation and the mean spherical model ͑MSM͒.  ... 
doi:10.1103/physreve.62.3640 pmid:11088864 fatcat:d7ac5juqtfgivnhhiriy6x2oby

A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging

Luc Florack, Evgeniya Balmashnova, Laura Astola, Ellen Brunenberg
2010 Journal of Mathematical Imaging and Vision  
previously required recourse to spherical harmonic decomposition.  ...  In particular it admits analytically closed form expressions for Tikhonov regularization schemes and estimation of an orientation distribution function via the Funk-Radon Transform in tensorial form, which  ...  Acknowledgements The Netherlands Organisation for Scientific Research (NWO) is gratefully acknowledged for financial support.  ... 
doi:10.1007/s10851-010-0217-3 fatcat:4mxbakvknbhvrpxy7732p2lkte

Magnetic dipole radiation tailored by substrates: numerical investigation [article]

Dmitry L. Markovich, Pavel Ginzburg, Anton Samusev, Pavel A. Belov,, Anatoly V. Zayats
2014 arXiv   pre-print
While the response of individual dielectric or metal spherical particles can be described analytically via multipole decomposition in the Mie series, the influence of substrates, in many cases present  ...  Optical properties of nanoparticles were characterized via scattering cross-section spectra, electric field profiles, and induced electric and magnetic moments.  ...  Optical response of individual spherical particles embedded in homogeneous host materials can be described 52 analytically via the Mie series decomposition [18] .  ... 
arXiv:1402.3911v1 fatcat:4rc2ijzs7bglbgortakm4qp5fm

Modelling effective dielectric properties of materials containing diverse types of biological cells

Sonja Huclova, Daniel Erni, Jürg Fröhlich
2010 Journal of Physics D: Applied Physics  
The numerical method is validated by comparing a model of spherical inclusions at a low volume fraction with the analytical solution obtained by the Maxwell-Garnett mixing formula, resulting in good agreement  ...  For the generation of the numerical models of the cells a flexible parametrization method based on the so-called superformula is applied including the option of obtaining non-axisymmetric shapes such as  ...  Another analytical method for modelling various kinds of shapes is the spectral decomposition method or the spectral density function approach (e.g. [11, 26, 27] ).  ... 
doi:10.1088/0022-3727/43/36/365405 fatcat:rfdyfhwp5jcjlheluvbv7liu3m

Analysis of Electromagnetic Scatterers Using Hybrid Higher Order FEM-MoM Technique

M. M. Ilić, S. V. Savić, A. Ž. Ilić, B. M. Notaroš
2009 Telfor Journal  
A higher order large-domain hybrid finite element – method of moments (FEM-MoM) technique is presented.  ...  The discretization and solving FEM and MoM parts of the problem and the coupling of the two methods are described.  ...  In this arrangement, for example, piecewise homogeneous dielectric domains can be modeled as MoM objects (via surface equivalence theorem) or as FEM regions.  ... 
doaj:73f6d56fa2224195a8ed5c6ee59c921c fatcat:mfkhtzmipzeodm6ffcpzh3ysxm
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