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## ‣ Análise de distúrbios relacionados com a qualidade da energia elétrica utilizando a transformada Wavelet; Analysis of power quality disturbances using Wavelet transform

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 07/04/2003
Português

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#Análise multiresolução#Classificação de distúrbios#Classifying disturbances#Multiresolution analysis#Power quality#Qualidade da energia#Transformada Wavelet#Wavelet transform

O presente trabalho visa a utilização da transformada Wavelet no monitoramento do sistema elétrico no que diz respeito a problemas de qualidade da energia com o intuito de detectar, localizar e classificar os mesmos. A transformada Wavelet tem surgido na literatura como uma nova ferramenta para análise de sinais, utilizando funções chamadas Wavelet mãe para mapear sinais em seu domínio, fornecendo informações simultâneas nos domínios tempo e freqüência. A transformada Wavelet é realizada através de filtros decompondo-se um dado sinal em análise multiresolução. Por esta, obtém-se a detecção e a localização de distúrbios relacionados com a qualidade da energia decompondo-se o sinal em dois outros que representam uma versão de detalhes (correspondente as altas freqüências do sinal) e uma versão de aproximação (correspondente as baixas freqüências do sinal). A versão de aproximação é novamente decomposta obtendo-se novos sinais de detalhes e aproximações e assim sucessivamente. Sendo assim, os distúrbios podem ser detectados e localizados no tempo em função do seu conteúdo de freqüência. Estas informações fornecem também características únicas pertinentes a cada distúrbio, permitindo classificá-los. Desta forma...

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## ‣ Aplicação de wavelets na análise de gestos musicais em timbres de instrumentos acústicos tradicionais.; Wavelets application on the analysis of musical gestures in timbres of traditional acoustic instruments.

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 11/09/1997
Português

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#Análise e síntese#Análise multiresolução#Analysis and synthesis#Gestos musicais#Multiresolution analysis#Music#Música#Musical gestures#Processamento de sinais#Signal processing#Wavelets

A expressividade é um elemento chave para o transporte de emoções em música, e seu modelamento, vital para a concepção de sistemas de síntese mais realistas. Gestos musicais executados durante a interpretação usualmente portam a informação responsável pela expressividade percebida, e podem ser rastreados por meio de padrões sônicos a eles associados em diversas escalas de resolução. Um conjunto relevante de gestos musicais expressivos foi estudado através de uma análise em multiresolução utilizando-se a transformada wavelet. A escolha deve-se principalmente à capacidade natural desta ferramenta em realizar análises de tempo-escala/frequência, e suas semelhanças com o processamento dos estágios primários do sistema auditivo. Vinte e sete eventos musicais foram capturados em interpretações de violino e flauta, e analisados com o objetivo de avaliar a aplicabilidade desta ferramenta na identificação e segregação de padrões sônicos associados a gestos musicais expressivos. Os algoritmos wavelet foram implementados na plataforma MATLAB utilizando-se bancos de filtros organizados em esquema piramidal. Rotinas para análises gráfica e sônica e uma interface ao usuário foram também implementadas. Verificou-se que as wavelets permitem a identificação de padrões sônicos associados a gestos expressivos exibindo diferentes propriedades em níveis diferentes da análise. A técnica mostrou-se útil para isolar ruídos oriundos de fontes diversas...

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## ‣ Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Fonte: Universidade Estadual Paulista
Publicador: Universidade Estadual Paulista

Tipo: Artigo de Revista Científica
Formato: 6213-6221

Português

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#Mammography#Polynomial classifier#Texture analysis#Wavelet CAD#Area under the ROC curve#Artificial intelligence algorithms#Classification algorithm#Digitized mammograms#Receiver operating characteristics curves (ROC)#Wavelet domain features#Algorithms

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

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## ‣ Adaptive multiresolution analysis based on anisotropic triangulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/01/2011
Português

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A simple greedy refinement procedure for the generation of data-adapted
triangulations is proposed and studied. Given a function of two variables, the
algorithm produces a hierarchy of triangulations and piecewise polynomial
approximations on these triangulations. The refinement procedure consists in
bisecting a triangle T in a direction which is chosen so as to minimize the
local approximation error in some prescribed norm between the approximated
function and its piecewise polynomial approximation after T is bisected.
The hierarchical structure allows us to derive various approximation tools
such as multiresolution analysis, wavelet bases, adaptive triangulations based
either on greedy or optimal CART trees, as well as a simple encoding of the
corresponding triangulations. We give a general proof of convergence in the Lp
norm of all these approximations.
Numerical tests performed in the case of piecewise linear approximation of
functions with analytic expressions or of numerical images illustrate the fact
that the refinement procedure generates triangles with an optimal aspect ratio
(which is dictated by the local Hessian of of the approximated function in case
of C2 functions).; Comment: 19 pages, 7 figures

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## ‣ Multiresolution Analysis of Incomplete Rankings

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/03/2014
Português

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Incomplete rankings on a set of items $\{1,\; \ldots,\; n\}$ are orderings of
the form $a_{1}\prec\dots\prec a_{k}$, with $\{a_{1},\dots
a_{k}\}\subset\{1,\dots,n\}$ and $k < n$. Though they arise in many modern
applications, only a few methods have been introduced to manipulate them, most
of them consisting in representing any incomplete ranking by the set of all its
possible linear extensions on $\{1,\; \ldots,\; n\}$. It is the major purpose
of this paper to introduce a completely novel approach, which allows to treat
incomplete rankings directly, representing them as injective words over $\{1,\;
\ldots,\; n\}$. Unexpectedly, operations on incomplete rankings have very
simple equivalents in this setting and the topological structure of the complex
of injective words can be interpretated in a simple fashion from the
perspective of ranking. We exploit this connection here and use recent results
from algebraic topology to construct a multiresolution analysis and develop a
wavelet framework for incomplete rankings. Though purely combinatorial, this
construction relies on the same ideas underlying multiresolution analysis on a
Euclidean space, and permits to localize the information related to rankings on
each subset of items. It can be viewed as a crucial step toward nonlinear
approximation of distributions of incomplete rankings and paves the way for
many statistical applications...

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## ‣ Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2007
Português

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#Mathematics - Numerical Analysis#Mathematics - Functional Analysis#42C40#41A05#42C15#47B99#65D10#94A08

In this paper, we propose a solution for a fundamental problem in
computational harmonic analysis, namely, the construction of a multiresolution
analysis with directional components. We will do so by constructing subdivision
schemes which provide a means to incorporate directionality into the data and
thus the limit function. We develop a new type of non-stationary bivariate
subdivision schemes, which allow to adapt the subdivision process depending on
directionality constraints during its performance, and we derive a complete
characterization of those masks for which these adaptive directional
subdivision schemes converge. In addition, we present several numerical
examples to illustrate how this scheme works. Secondly, we describe a fast
decomposition associated with a sparse directional representation system for
two dimensional data, where we focus on the recently introduced sparse
directional representation system of shearlets. In fact, we show that the
introduced adaptive directional subdivision schemes can be used as a framework
for deriving a shearlet multiresolution analysis with finitely supported
filters, thereby leading to a fast shearlet decomposition.; Comment: 35 pages, 7 figures

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## ‣ Wavelets, Curvelets and Multiresolution Analysis Techniques Applied to Implosion Symmetry Characterization of ICF Targets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/11/2012
Português

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We introduce wavelets, curvelets and multiresolution analysis techniques to
assess the symmetry of X ray driven imploding shells in ICF targets. After
denoising X ray backlighting produced images, we determine the Shell Thickness
Averaged Radius (STAR) of maximum density, r*(N, {\theta}), where N is the
percentage of the shell thickness over which to average. The non-uniformities
of r*(N, {\theta}) are quantified by a Legendre polynomial decomposition in
angle, {\theta}. Undecimated wavelet decompositions outperform decimated ones
in denoising and both are surpassed by the curvelet transform. In each case,
hard thresholding based on noise modeling is used. We have also applied
combined wavelet and curvelet filter techniques with variational minimization
as a way to select the significant coefficients. Gains are minimal over
curvelets alone in the images we have analyzed.; Comment: 6 pages, 4 figures, IFSA Conference 2003 Proceedings, p107, B. A.
Hammel, D. D. Meyerhofer, J. Meyer-ter-Vehn and H. Azechi, editors, American
Nuclear Society, 2004

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## ‣ Wavelets, Curvelets and Multiresolution Analysis Techniques in Fast Z Pinch Research

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/11/2012
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Z pinches produce an X ray rich plasma environment where backlighting imaging
of imploding targets can be quite challenging to analyze. What is required is a
detailed understanding of the implosion dynamics by studying snapshot images of
its in flight deformations away from a spherical shell. We have used wavelets,
curvelets and multiresolution analysis techniques to address some of these
difficulties and to establish the Shell Thickness Averaged Radius (STAR) of
maximum density, r*(N, {\theta}), where N is the percentage of the shell
thickness over which we average. The non-uniformities of r*(N, {\theta}) are
quantified by a Legendre polynomial decomposition in angle, {\theta}, and the
identification of its largest coefficients. Undecimated wavelet decompositions
outperform decimated ones in denoising and both are surpassed by the curvelet
transform. In each case, hard thresholding based on noise modeling is used.; Comment: 11 pages, 17 figures, Volume 5207 Wavelets: Applications in Signal
and Image Processing X. 10.1117/12.506243

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## ‣ Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of $L^2({\mathbb R})$

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/05/2009
Português

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Spectral representations of the dilation and translation operators on
$L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets
and multiresolution analysis are then described in terms of rigid
operator-valued functions defined on the functional spectral spaces. The
approach is useful for computational purposes.; Comment: 26 pages

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## ‣ Multiresolution wavelet analysis of Bessel functions of scale $\nu +1$

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Functional Analysis#Mathematical Physics#42C15, 43A99, 44A20, 81R50 (Primary)#46N50,47D45, 47D25 (Secondary)

We identify multiresolution subspaces giving rise via Hankel transforms to
Bessel functions. They emerge as orthogonal systems derived from geometric
Hilbert-space considerations, the same way the wavelet functions from a
multiresolution scaling wavelet construction arise from a scale of Hilbert
spaces. We study the theory of representations of the C*-algebra O_{\nu+1}
arising from this multiresolution analysis.; Comment: 19 pages, REVTeX v. 3.1, submitted to J. Math. Phys., PACS 02.30.Nw,
02.30.Tb, 03.65.-w, 03.65.Bz, 03.65.Db. In the revision, the title is changed
(from "Deformed multiresolution wavelet analysis of scale $\nu +1$"), some
more introductory material is added, and some points both in the statements
of results and their proof have been clarified

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## ‣ Multiresolution analysis for Markov Interval Maps

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2011
Português

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We set up a multiresolution analysis on fractal sets derived from limit sets
of Markov Interval Maps. For this we consider the $\mathbb{Z}$-convolution of a
non-atomic measure supported on the limit set of such systems and give a
thorough investigation of the space of square integrable functions with respect
to this measure. We define an abstract multiresolution analysis, prove the
existence of mother wavelets, and then apply these abstract results to Markov
Interval Maps. Even though, in our setting the corresponding scaling operators
are in general not unitary we are able to give a complete description of the
multiresolution analysis in terms of multiwavelets.; Comment: 31 pages, 4 figures

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## ‣ Multiresolution Analysis Based on Coalescence Hidden-variable FIF

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/01/2012
Português

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In the present paper, multiresolution analysis arising from Coalescence
Hidden-variable Fractal Interpolation Functions (CHFIFs) is accomplished. The
availability of a larger set of free variables and constrained variables with
CHFIF in multiresolution analysis based on CHFIFs provides more control in
reconstruction of functions in L2(\mathbb{R})than that provided by
multiresolution analysis based only on Affine Fractal Interpolation Functions
(AFIFs). In our approach, the vector space of CHFIFs is introduced, its
dimension is determined and Riesz bases of vector subspaces Vk, k \in
\mathbb{Z}, consisting of certain CHFIFs in L2(\mathbb{R}) \cap C0(\mathbb{R})
are constructed. As a special case, for the vector space of CHFIFs of dimension
4, orthogonal bases for the vector subspaces Vk, k \in \mathbb{Z}, are
explicitly constructed and, using these bases, compactly supported continuous
orthonormal wavelets are generated.; Comment: 19 Pages, 3 Figures

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## ‣ A new multiresolution finite element method based on a multiresolution quadrilateral plate element

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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A new multiresolution quadrilateral plate element is proposed and a
multiresolution finite element method is hence presented. The multiresolution
analysis (MRA) framework is formulated out of a mutually nesting displacement
subspace sequence, whose basis functions are constructed of scaling and
shifting on the element domain of basic node shape function. The basic node
shape function is constructed by extending shape function around a specific
node. The MRA endows the proposed element with the resolution level (RL) to
adjust the element node number, thus modulating structural analysis accuracy
accordingly. As a result, the traditional 4-node quadrilateral plate element
and method is a monoresolution one and also a special case of the proposed
element and method. The meshing for the monoresolution plate element model is
based on the empiricism while the RL adjusting for the multiresolution is laid
on the rigorous mathematical basis. The accuracy of a structural analysis is
actually determined by the RL, not by the mesh. The rational MRA enable the
implementation of the multiresolution element method to be more rational and
efficient than that of the conventional monoresolution plate element method or
other corresponding MRA methods such as the wavelet finite element method...

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## ‣ A Multiresolution Ensemble Kalman Filter using Wavelet Decomposition

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/11/2015
Português

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We present a method of using classical wavelet based multiresolution analysis
to separate scales in model and observations during data assimilation with the
ensemble Kalman filter. In many applications, the underlying physics of a
phenomena involve the interaction of features at multiple scales. Blending of
observational and model error across scales can result in large forecast
inaccuracies since large errors at one scale are interpreted as inexact data at
all scales. Our method uses a transformation of the observation operator in
order to separate the information from different scales of the observations.
This naturally induces a transformation of the observation covariance and we
put forward several algorithms to efficiently compute the transformed
covariance. Another advantage of our multiresolution ensemble Kalman filter is
that scales can be weighted independently to adjust each scale's effect on the
forecast. To demonstrate feasibility we present applications to a one
dimensional Kuramoto-Sivashinsky (K-S) model with scale dependent observation
noise and an application involving the forecasting of solar photospheric flux.
The latter example demonstrates the multiresolution ensemble Kalman filter's
ability to account for scale dependent model error. Modeling of photospheric
magnetic flux transport is accomplished by the Air Force Data Assimilative
Photospheric Transport (ADAPT) model.

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## ‣ Fault Analysis Using Gegenbauer Multiresolution Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/02/2015
Português

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This paper exploits the multiresolution analysis in the fault analysis on
transmission lines. Faults were simulated using the ATP (Alternative Transient
Program), considering signals at 128/cycle. A nonorthogonal multiresolution
analysis was provided by Gegenbauer scaling and wavelet filters. In the cases
where the signal reconstruction is not required, orthogonality may be
immaterial. Gegenbauer filter banks are thereby offered in this paper as a tool
for analyzing fault signals on transmission lines. Results are compared to
those ones derived from a 4-coefficient Daubechies filter. The main advantages
in favor of Gegenbauer filters are their smaller computational effort and their
constant group delay, as they are symmetric filters.; Comment: 6 pages, 12 figures. In: Transmission and Distribution IEEE/PES/T&D
Latin America, Sao Paulo, Brazil, 2004

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## ‣ A Family of Wavelets and a new Orthogonal Multiresolution Analysis Based on the Nyquist Criterion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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A generalisation of the Shannon complex wavelet is introduced, which is
related to raised cosine filters. This approach is used to derive a new family
of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic
Interference (ISI) elimination. An orthogonal Multiresolution Analysis (MRA) is
presented, showing that the roll-off parameter should be kept below 1/3. The
pass-band behaviour of the Wavelet Fourier spectrum is examined. The left and
right roll-off regions are asymmetric; nevertheless the Q-constant analysis
philosophy is maintained. Finally, a generalisation of the (square root) raised
cosine wavelets is proposed.; Comment: 8 pages, 14 figures

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## ‣ A hypergeometric basis for the Alpert multiresolution analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Mathematics - Classical Analysis and ODEs#Mathematics - Functional Analysis#Mathematics - Numerical Analysis

We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$
hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier
transform of each basis function is written in terms of ${}_2F_3$
hypergeometric functions. Moreover, the entries in the matrix equation
connecting the wavelets with the scaling functions are shown to be balanced
${}_4 F_3$ hypergeometric functions evaluated at $1$, which allows to compute
them recursively via three-term recurrence relations.
The above results lead to a variety of new interesting identities and
orthogonality relations reminiscent to classical identities of higher-order
hypergeometric functions and orthogonality relations of Wigner $6j$-symbols.

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## ‣ Shannon Multiresolution Analysis on the Heisenberg Group

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We present a notion of frame multiresolution analysis on the Heisenberg
group, abbreviated by FMRA, and study its properties. Using the irreducible
representations of this group, we shall define a sinc-type function which is
our starting point for obtaining the scaling function. Further, we shall give a
concrete example of a wavelet FMRA on the Heisenberg group which is analogous
to the Shannon
MRA on $\RR$.; Comment: 17 pages

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## ‣ An adaptive numerical method for the Vlasov equation based on a multiresolution analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/04/2007
Português

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In this paper, we present very first results for the adaptive solution on a
grid of the phase space of the Vlasov equation arising in particles accelarator
and plasma physics. The numerical algorithm is based on a semi-Lagrangian
method while adaptivity is obtained using multiresolution analysis.

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## ‣ Boundary element based multiresolution shape optimisation in electrostatics

Fonte: Elsevier
Publicador: Elsevier

Tipo: Article; published version

Português

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#Shape optimisation#Shape derivative#Boundary element method#Subdivision surfaces#Multiresolution analysis

This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jcp.2015.05.017; We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.; We gratefully acknowledge the support provided by the EU commission through the FP7 Marie Curie IAPP project CASOPT (PIAP-GA-2008-230224). K.B. and F.C. thank for the additional support provided by EPSRC through #EP/G008531/1. J.Z. thanks for the support provided by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the project SPOMECH ? Creating a Multidisciplinary R&D Team for Reliable Solution of Mechanical Problems...

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