in this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). the solution of the problem includes two main parts. in the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. in the second part, ada...

We construct interpolating divergence-free multiwavelets based on cubic Hermite splines. We give characterizations of the relevant function spaces and indicate their use for analyzing experimental data of incompressible flow fields. We also show that the standard interpolatory wavelets, based on the Deslauriers-Dubuc interpolatory scheme or on interpolatory splines, cannot be used to construct ...

In this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams). The solution of the problem includes two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, ada...

We consider a method of adapting Dubuc-Deslauriers sudivision, which is de ̄ned for bi-in ̄nite sequences, to accommodate sequences of ̄nite length. After deriving certain useful properties of the Dubuc-Deslauriers re ̄nable function on R, we de ̄ne a multi-scale ̄nite sequence of functions on a bounded interval, which are then proved to be re ̄nable. Using this fact, the resulting adapted interpolato...

In many applications, wavelets are usually expected to have the following properties: compact support, orthogonality, linear-phase, regularity, and interpolation. To construct such wavelets, it is crucial designing scaling functions with the above properties. In twoand three-band cases, except for the Haar functions, there exists no scaling function with the above five properties. In -band case...

We describe bases of smooth wavelets where the coe cients are obtained by integration against ( nite combinations of) boxcar kernels rather than against traditional smooth wavelets. Bases of this type were rst developed in work of Tchamitchian and of Cohen, Daubechies, and Feauveau. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having pre...

The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from B-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provi...

ABSTRAC:In this technological field, image storage is happening through the personal computer. A medical doctor can make a diagnosis using a full three – dimensional image on a computer screen – not long ago surgery would have been necessary to capture the same critical point of view. Satellite images of earth and places beyond is been continually transmitted over communication channels. The In...

Net subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc-Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interp...