Fast wavelet transforms for matrices arising from boundary element methods

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Cornell Theory Center, Cornell University , Ithaca, N.Y
StatementDave M. Bond, Stephen A. Vavasis.
SeriesTechnical report / Cornell Theory Center -- CTC94TR174., Technical report (Cornell Theory Center) -- 174.
ContributionsVavasis, Stephen A., Cornell Theory Center.
The Physical Object
Pagination45 p. :
ID Numbers
Open LibraryOL17790698M
OCLC/WorldCa33985298

@MISC{Bond94fastwavelet, author = {Dave M. Bond and Stephen A. Vavasis}, title = {Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods}, year = {}} Share.

OpenURL. Abstract. For many boundary element methods applied to Laplace's equation in two dimensions, the resulting integral equation has both an integral with a. Fast Wavelet Transforms for Matrices Arising from Boundary Element Methods. For many boundary element methods applied to Laplace's equation in two dimensions, the resulting integral equation has both an integral with a logarithmic kernel and an integral with a discontinuous kernel.

If standard collocation methods are used to discretize the Author: David M. Bond and Stephen A. Vavasis. A new preconditioning strategy is introduced for finger pattern matrices arising from the application of the discrete wavelet transform to discretisations of BIEs. The new strategy is compared against some existing preconditioning strategies and its advantage is demonstrated for low bandwidth preconditioners, and for problems witho diagonal Author: Stuart C.

Hawkins, Ke Chen. – The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems., – The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices.

Wavelets are then used again to produce an algorithm to solve the resultant sparse Cited by: 2. Methods Engng. 19 () ] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form.

This paper describes application of fast wavelet transforms in the boundary element method to solve 2D elasticity problems. Daubechies compactly supported orthogonal wavelets have been applied to compress dense and fully populated matrices arising from BEM.

GMRES solver is then used to solve linear algebraic systems. 1. Introduction. The solution of very large problems arising from the Boundary Element Method (BEM) is still a big challenge for most industrial application developers due to the O(N 2) growth of the system matrices as the number of degrees of freedom in the model l methods were suggested, where this explosive growth is substituted by a less restrictive behavior of order O.

() an operator splitting preconditioner for matrices arising from a wavelet boundary element method for the helmholtz equation.

Details Fast wavelet transforms for matrices arising from boundary element methods PDF

International Journal of Wavelets, Multiresolution and Information Processing   Purpose – The purpose of this paper is to introduce a novel approach to solving linear systems arising from applying a Boundary Element Method (BEM) to elasticity problems.

Design/methodology/approach – The key idea is based on using wavelet transforms as a tool to change dense and fully populated matrices of BEM systems into sparse matrices.

Wavelets are then used. In this paper we consider a wavelet algorithm for the piecewise constant collocation method applied to the boundary element solution of a first kind integral equation arising in acoustic scattering.

The conventional stiffness matrix is transformed into the corresponding matrix with respect to wavelet bases, and it is approximated by a. The structure of wavelet transforms like the Daubechies D4 transform can be more clearly explained in the context of linear algebra (e.g., matrices).

Wavelet algorithms like the Daubechies D4 transform have special cases that must be handled in real applications with finite data sets.

Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods. For many boundary element methods applied to Laplace's equation in two dimensions, the resulting integral equation has both an integral with a logarithmic kernel and an integral with a discontinuous kernel.

If standard collocation methods are used to. Bond, D. M., & Vavasis, S. Fast Wavelet Transforms for Matrices Arising from Boundary Element Methods.

Cornell Theory Center, Cornell University. An operator splitting type preconditioner is presented for fast solution of linear systems obtained by Galerkin discretization of the Burton and Miller formulation for the Helmholtz equation. Our approach differs from usual boundary element treatments of the three-dimensional scattering problem because we use a basis of biorthogonal wavelets.

DOI: /cpa Corpus ID: Fast wavelet transforms and numerical algorithms I @article{BeylkinFastWT, title={Fast wavelet transforms and numerical algorithms I}, author={Gregory Beylkin and Ronald R.

Coifman and Vladimir Rokhlin}, journal={Communications on Pure and Applied Mathematics}, year={}, volume={44}, pages={} }. Fast Wavelet Transforms and Numerical Algorithms I G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN Yale University Abstract A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors.

Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow.

These methods are typically iterative, based on coupling fast matrix-vector multiplication routines with conjugate-gradient-type schemes. Here, we discuss methods that are currently under development for the fast, direct solution of boundary integral equations in three dimensions.

Biorthogonal wavelet bases for the boundary element method of the fast wavelet transform also for its inverse.

This is an important task for the coupling of FEM and BEM, the main diagonal of the system matrix defines a simple preconditioningfor the linear system of equations arising from boundary integral operators of nonzero order [6.

Abstract: A fast non-similarity wavelet transform method, proposed earlier by the authors, is further studied. Combined with conventional techniques such as the method of moments, the boundary element method and the finite element method, the wavelet transform method can effectively handle a wide range of complicated problems which involve various complex media and conductors.

shapes, strains or stresses. In this article, the methods based on Wavelet Transform associated with the boundary element technique will be combined with the scope to detect the position of a damage just using the damaged response of the actual structure. After presenting the formulation, numerical.

Wavelet compression. Wavelet compression is a form of data compression well suited for image compression (sometimes also video compression and audio compression).Notable implementations are JPEGDjVu and ECW for still images, CineForm, and the BBC's goal is to store image data in as little space as possible in a t compression can be either lossless or lossy.

Bond and S. Vavasis, "Fast Wavelet Transforms for Matrices Arising From Boundary Element Methods." T. Chan, W. Tang and W. Wan. Charton and V. Perrier, "Factorisation sur Bases d'Ondelettes du Noyeau de la Chaleur et Algorithmes Matriciels Rapides Associes.".

An element free boundary point method based on wavelet radial basis functions. Preliminary report. John R. Williams* and Kevin Amaratunga, Massachusetts Institute of Technology Bond, D. Fast wavelet transforms for matrices arising from boundary element methods. wt = cwt(x) returns the continuous wavelet transform (CWT) of input, x, is a real- or complex-valued vector, or a single-variable regularly sampled timetable, and must have at least four CWT is obtained using the analytic Morse wavelet with the symmetry parameter (gamma) equal to 3 and the time-bandwidth product equal to Key words: boundary integral equations, boundary element method, wavelet bases, matrix compression Abstract This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations.

Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. where: f a is the frequency associated with the wavelet at the specific a scale, while f c is the characteristic frequency of mother wavelet at scale a = 1, and time position b = 0.

There is a very important distinction to be made here: “The characteristic frequency f c of the wavelet used in the wavelet transform is representative of the whole frequency makeup of the wavelet. 33 [Bellman et al()] was an early review book on numerical Laplace transform inversion for linear 34 and non-linear problems, but without the benefit of the many algorithms that have since been devel- 35 oped.

[Davies and Martin()] performed a thorough survey, assessing numerical Laplace transform in version algorithm accuracy for techniques available inusing simple. The Wavelet Element Method.

Description Fast wavelet transforms for matrices arising from boundary element methods FB2

Applied and Computational Harmonic Analysis, Vol. 6, Issue. 1, p. ‘ Fast wavelet transforms and numerical algorithms I ’, ‘ On the fast matrix multiplication in the boundary element method by panel clustering ’, Numer. Math. 54, The usually used fast wavelet transform (FWT) has its inconvenience in application.

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One frequently met problem is that FWT is rarely realized in the form of linear transformation by matrix and vector multiplication, which is the form that almost all the other existing orthogonal transforms take.

The Haar transform can be used for image compression. The basic idea is to transfer the image into a matrix in which each element of the matrix represents a pixel in the image. For example, a × matrix is saved for a × image. JPEG image compression involves cutting the original image into 8×8 sub-images.

Each sub-image is an 8×8. The output decomposition structure consists of the wavelet decomposition vector C and the bookkeeping matrix S, which contains the number of coefficients by level and orientation.

[ C, S ] = wavedec2(X, N, Lod,Hid) returns the wavelet decomposition using the specified lowpass and highpass decomposition filters LoD and HiD, respectively.The Fast Wavelet Transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain.Fast Boundary Element Methods in Approximate hierarchical Cholesky decomposition of sparse matrices arising from curl–curl equation Mittag – Kaffee fast techniques such as hierarchical matrices, the multipole method or wavelet ma-trix compression, which will be .