A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.

An estimate is given for the support of each component function of a compactly supported scaling vector satisfying a matrix refinement equation with finite number of terms. The estimate is based on the highest and lowest degree of each polynomial in the corresponding matrix symbol. Only basic techniques from matrix theory are involved in the derivation.

Development of system software by refinement has been extensively studied, and few larger scale case studies has been carried out. Most refinement approaches havse relied on manual construction of ad-hoc non-reusable refinements that are subjected to post-hoc verification. The problem with this approach is that the incremental cost of adapting to changing requirements is too high for this to be...

We consider a family of d×d matrices We indexed by e ∈ E where (E,μ) is a probability space and some natural conditions the family (We)e∈E are satisfied. The aim of this paper is to develop a theory of continuous, compactly supported functions φ : R → C which satisfy a refinement equation of the form φ(x) = Z

We consider adaptive meshless discretisation of the Dirichlet problem for Poisson equation based on numerical differentiation stencils obtained with the help of radial basis functions. New meshless stencil selection and adaptive refinement algorithms are proposed in 2D. Numerical experiments show that the accuracy of the solution is comparable with, and often better than that achieved by the me...

In this survey paper, some of the basic properties of multiwavelets are reviewed. Particular emphasis is given to approximation-theoretic issues and sampling on compact intervals. In addition, a translation invariant multiwavelet transform is discussed and the regularity and approximation order of the associated correlation matrices, which satisfy a particular matrix-valued refinement equation,...

Compact objects combine a wide array of fascinating physics, and gravitational waves may open new ways to probe these objects. We are interested in systems where gravitational and magnetic fields are dynamically important. One challenge in simulating astrophysical compact objects is that these systems require a range of important length and time scales. Adaptive mesh refinement (AMR) thus becom...

Purpose This study aims to explicate the behavioral factors that determine willingness share personal health data for secondary uses. Design/methodology/approach A theoretical model is developed and tested with structural equation modeling using survey from Finland. Findings It shown attitude toward information sharing strongest factor contributing (PHI). Trust control serve as mediating betwee...

We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter, described by the Schrödinger-Poisson (SP) equation with a particle mass ∼10(-22)  eV. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark ma...