In this paper we introduce multiresolution analysis (MRA) algorithms intended to be used in scientific visualization, and based on a non-nested set of approximatingspaces. The need for non nested spaces arises from the fact that the required scaling functions do not fulfill any refinement equation. Therefore we introduce in the first part the concept of approximated refinement equation, that al...

The purpose of this paper is to investigate spectral properties of the transition operator associated to a multivariate vector refinement equation and their applications to the study of smoothness of the corresponding refinable vector of functions. Let Φ = (φ1, . . . , φr) be an r× 1 vector of compactly supported functions in L2(IR) satisfying the refinement equation Φ = ∑ α∈Z s a(α)Φ(M · − α),...

The fundamental solution of the Laplace equation in two dimensions is not contained in the Sobolev space H1(Ω) such that finite element error estimates are non-standard and quasi-uniform meshes are inappropriate. By using graded meshes L2-error estimates of almost optimal order are shown. As a by-product, we show for the Poisson equation with a right-hand side in L2 that appropriate mesh refine...

Three iterative refinement schemes are studied for approximating the solutions of linear weakly singular Fredholm integral equations of the second kind. The rates of convergence and computational costs of the three schemes are studied and compared with the classical approach by applying them respectively to: (i) a sparse linear system associated with an integral equation modelling a real life A...

Error estimates for the space-semidiscrete approximation of solutions of the wave equation in polygons G ⊂ R are presented. Based on corner asymptotics of solutions of the wave equation, it is shown that for continuous, simplicial Lagrangian Finite Elements of polynomial degree p ≥ 1 with either suitably graded mesh refinement or with bisection tree mesh refinement towards the corners of G, the...

The thesis aims to solve partial differential equations numerically using mimetic spectral element method. The method rewrites the PDEs with differential forms so the resulting equations are able to preserve geometrical characteristics in physics. The equation we focus is the Poisson equation, which can be utilized for potential flow problems. The physical domain to be tested is a typical flow ...

The extensive research leveraging RGB-D information has been exploited in salient object detection. However, visual cues appear various scales and resolutions of RGB images due to semantic gaps at different feature levels. Meanwhile, similar patterns are available cross-modal depth as well multi-scale versions. Cross-modal fusion refinement still an open problem detection task. In this paper, w...