The scattering by a pair of spatially disjoint local regions of complex (multiscale) stiiness heterogeneity in an unbounded thin linearly elastic plate, is investigated. Issues of the mutual interaction of the spatially disjoint scatterers and its manifestation within a homogenized, or eeective, formulation governing large scale response elds, are the focus. It is shown analytically and numeric...

The multiresolution analysis (MRA) strategy for the reduction of a nonlinear differential equation is a procedure for constructing an equation directly for the coarse scale component of the solution. The MRA homogenization process is a method for building a simpler equation whose solution has the same coarse behavior as the solution to a more complex equation. We present two multiresolution red...

Wavelets are generated from refinable functions by using multiresolution analysis. In this paper we investigate the smoothness properties of multivariate refinable functions in Sobolev spaces. We characterize the optimal smoothness of a multivariate refinable function in terms of the spectral radius of the corresponding transition operator restricted to a suitable finite dimensional invariant s...

In this paper, we propose a novel mesh deformation approach via manipulating differential properties non-uniformly. Guided by user-specified material properties, our method can deform the surface mesh in a non-uniform way while previous deformation techniques are mainly designed for uniform materials. The non-uniform deformation is achieved by material-dependent gradient field manipulation and ...