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
On the Adaptive Numerical Solution of Nonlinear Partial Differential Equations in Wavelet Bases
Gregory Beylkin,James M. Keiser +1 more
TL;DR: In this paper, fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form = Lu+ Nf(u), where L and N are linear differential operators and f(u) is a nonlinear function are developed.
167
A wavelet based space-time adaptive numerical method for partial differential equations
TL;DR: In this paper, a schema numerique adaptatif en espace and en temps, utilisant les bases orthonormales d'ondelettes, is presented for the resolution d'equations aux derivees partielles.
Adaptive wavelet collocation method for the solution of Burgers equation
TL;DR: In this paper, an adaptive wavelet method was applied to numerical solution of the viscous Burgers equation, which is based on a collocation of the wavelet and the velocity of the Burgers.
60
Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval
Silvia Bertoluzza,Giovanni Naldi,Jean Christophe Ravel +2 more
- 01 Jan 1994
TL;DR: This work will concentrate on the elliptic case where some methods specially suited to treat Dirichlet's boundary conditions are tested, among them a Galerkin method based on the wavelets on the interval of [9] and a wavelet collocation method.
55
On the wavelet optimized finite difference method
Leland Jameson
- 01 Mar 1994
TL;DR: In this paper, a wavelet-optimized finite difference method for solving nonlinear conservation laws is proposed. But it does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space.