2 edition of wavelet-optimized, very high order adaptive grid and order numerical method found in the catalog.
wavelet-optimized, very high order adaptive grid and order numerical method
Leland M. Jameson
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
|Series||ICASE report ;, no. 96-30, NASA contractor report ;, 198331, NASA contractor report ;, NASA CR-198331.|
|Contributions||Institute for Computer Applications in Science and Engineering.|
|LC Classifications||TL521.3.C6 A3 no. 198331|
|The Physical Object|
|Pagination||iii, 38 p. :|
|Number of Pages||38|
|LC Control Number||97188545|
In this study, an improved wavelet-based adaptive-grid method is presented for solving the second order hyperbolic Partial Differential Equations (PDEs) for describing the waves propagation in Abstract. A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of ://
In order to quantify the “order” of accuracy of our mesh refinement procedure, we make use of a projection to a uniform grid through an interpolation strategy similar to the ones described in the works of Deiterding et al 69 and Tenaud and Duarte. 70 Our adapted grid solution is projected to a uniform grid at the finest level of resolution high order scheme in order to equal one time step of the adaptive scheme at the coarse scale, 2J &TS=-N’ where TS denotes number of time steps. So we must take, (11) (12) time steps on the high order grid in order to equal one time step on the coarse scale grid. We, therefore, require that 2J —*: ‘* b* O~*Ot>~R(:)d2J-j *O. *Ot. a j=o 3 ?doi=&rep=rep1&type=pdf.
Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems I. Fatkullin1 and J. S. Hesthaven2 Received Febru ; accepted (in revised form) Ap We discuss a scheme for the numerical solution of one-dimensional initial value problems exhibiting strongly localized solutions or finite-time singularities. ~ibrahim/ When describing the anisotropic evolution of microstructures in solids using phase-field models, the anisotropy of the crystalline phases is usually introduced into the interfacial energy by directional dependencies of the gradient energy coefficients. We consider an alternative approach based on a wavelet analogue of the Laplace operator that is intrinsically anisotropic and ://
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This paper extends the numerical wavelet-optimized finite difference (WOFD) method to arbitrarily high order, so very high order adaptive grid and order numerical method book one obtains, in effect, an adaptive grid and adaptive order numerical method which can achieve errors equivalent to errors obtained with a "spectrally accurate" numerical :// Next, the issue of proper grids for high order polynomials is addressed.
Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the diggerencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of reginement the grid is a ?doi= A WAVELET-OPTIMIZED, VERY HIGH ORDER ADAPTIVE GRID and ORDER NUMERICAL METHOD.
an adaptive numerical method is introduced which adapts the numerical grid and the order of the diggerencing operator depending on the data.
The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of reginement the grid is a Chebyshe On the Wavelet-Optimized Finite Difference Method () 11 L. Jameson, A wavelet-optimized, very high order adaptive grid and order numerical method, SIAM J. Sci.
:// The main aim of wavelet-based numerical methods for solving partial differential equations is to develop adaptive schemes, in order to achieve accuracy and computational efficiency. The wavelet optimized finite difference method (WOFD) uses wavelets to generate appropriate grids to apply finite difference :// A WAVELET-OPTIMIZED, VERY HIGH ORDER ADAPTIVE GRID and ORDER NUMERICAL METHOD(Proceedings of the 14th NAL Symposium on Aircraft Computational Aerodynamics) Jameson Leland 航空宇宙技術研究所特別資料 34, A WAVELET-OPTIMIZED, VERY HIGH ORDER ADAPTIVE GRID and ORDER NUMERICAL METHOD Leland Jameson 1 Mitsubishi Heavy Industries, Ltd.
Advanced Technology Research CenterSachiura, 1-Chome, Kanazawa-ku, Yokohama,Japan email: lmj@ ABSTRACT Differencing operators of arbitrarily high order can be constructed by in- An adaptive numerical method for solving partial differential equations is developed.
The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O (N) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition The adaptive meshfree spectral graph wavelet method (AMSGWM) will use radial basis functions (RBFs) for interpolation of functions and for approximation of the differential operators.
The theory of interpolation of continuous functions by RBFs is well understood , , , , , . A Wavelet Optimized Adaptive Multi-Domain Method J. Hesthaven Brown University and L. Jameson To extend the wavelet based grid and order adaptation to multi-dimensional and geometrically complex numerical grid resolution or the sampling frequency in a signal processing scenario.
Hence, on a ?doi=&rep=rep1&type=pdf. here a two-dimensional version of a numerical method that we have named the Wavelet Optimized Finite Dif-ference Adaptive High Order (WOFD-AHO) method. WOFD-AHO dynamically moves with the data and fo-cuses in on the data at the appropriate scale to resolve whatever scales are present.
Furthermore, WOFD-AHO is fourth order in both space and  L. Jameson, “A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method”, Accepted SIAM J. Sci. Comput., and ICASE Report No.  Kagimoto, T and Yamagata, T, Seasonal Transport Variations of the Kuroshio: An OGCM Simulation, Journal of Physical Oceanography, 27,A wavelet optimized, very high order adaptive grid and order numerical method, ().
An Introduction to wavelets, Academic press, A wavelet analysis is utilized at regular intervals to adaptively select the order and the grid in accordance with the local behavior of the solution. Bacry, E., Mallat, S., and Papanicolaou, G. A wavelet based space-time adaptive numerical method for partial differential equations.
A wavelet-optimized, very high order A method is presented for adaptively solving hyperbolic PDEs. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids.
The adaptability is performed automatically by thresholding the wavelet coefficients. Operations such as differentiation and multiplication are fast and simple due to the one-to-one correspondence between point values and Numerical Studies of Wavelet-based Method as an Alternative Solution for Population Balance Problems in a Batch Crystalliser Johan Utomo, Tonghua Zhang, Nicoleta Balliu and Moses O.
Tadé* Department of Chemical Engineering, Curtin University of Technology, GPO Box UPerth, WAAustralia *corresponding author:(Tel ; e-mail: [email protected]). () A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method. SIAM Journal on Scientific ComputingAbstract | PDF ( KB) This paper extends the numerical wavelet-optimized finite di#erence (WOFD) method to arbitrarily high order, so that one obtains, in e#ect, an adaptive grid and adaptive order numerical method A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method, ICASE Report No.
96–30, and SIAM J. Sci. Comput. 19(6), – Google Scholar :// The crude spatial discretization introduces a large amount of numerical diffusion into the system, which, in combination with strong flow stretching, causes large numerical errors.
To resolve this issue, we have developed an optimized wavelet‐based adaptive mesh refinement (OWAMR) ://. Download Citation | Other Wavelet-Based Numerical Methods: A First Course | Systematically, wavelet-based methods for solving PDEs can be separated into the following categories in a very broad Adaptive Mesh Refinement (AMR) schemes are generally considered promising because of the ability of the scheme to place grid points or computational degrees of freedom at the location in the flow where truncation errors are unacceptably large.
For a given order, AMR schemes can reduce work. However, for the computation of turbulent or non-turbulent mixing when compared to high order non The adaptive method takes advantage of an interpolating wavelet for the adaptive approximation in the design of a simple refinement strategy that reflects the local demand of the physical solution.
The derivative approximation is computed via consistent finite-difference approximation on an adaptive ://