Open AccessJournal Article
Solving hyperbolic pdes using interpolating wavelets
167
TL;DR: In this paper, a method based on an interpolating wavelet transform using polynomial interpolation on dyadic grids is presented for adaptively solving hyperbolic PDEs.
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Abstract: 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 wavelet coefficients in the interpolating basis. Treatment of boundary conditions is simplified in this sparse point representation (SPR). Numerical examples are presented for one- and two-dimensional problems. It is found that the proposed method outperforms a finite difference method on a uniform grid for certain problems in terms of flops.
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References
Numerical Algorithms Based on Biorthogonal Wavelets
Pj. Ponenti,Jacques Liandrat +1 more
- 01 Feb 1996
TL;DR: In this article, a wavelet base is used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems, and an approximate solution is then stable and converges towards the exact solution.
12
Interpolation through an iterative scheme
TL;DR: In this article, a new method of interpolation was generated through an iterative scheme on dyadic rationals, which is linear, local and produces almost twice differentiable functions. Error formulas are derived.
A multilevel wavelet collocation method for solving partial differential equations in a finite domain
TL;DR: In this article, a multilevel wavelet collection method for the solution of partial differential equations is developed, which is tested on the one-dimensional Burgers equation with small viscosity.
An Adaptive Wavelet-Vaguelette Algorithm for the Solution of PDEs
Jochen Fröhlich,Kai Schneider +1 more
TL;DR: A fast algorithm for the discrete orthonormal wavelet transform and its inverse without using the scaling function is described and an improved construction employing the cardinal function of the multiresolution is presented.
Adaptive Multiresolution Schemes for Shock Computations
TL;DR: Adapt multiresolution schemes for the computation of discontinuous solutions of hyperbolic conservation laws are presented and the data compression of the numerical solution is used in order to reduce the number of numerical flux evaluations.