The main focus of this paper is to suggest a domain decomposition method for finite element approximations of elliptic problems with anisotropic coefficients in domains consisting of anisotropic shape rectangles. The theorems on traces of functions from Sobolev spaces play an important role in studying boundary value problems of partial differential equations. These theorems are commonly used f...

Posing objects in their upright orientations is the very first step of 3D shape analysis. However, 3D models in existing repositories may be far from their right orientations due to various reasons. In this paper, we present a data-driven method for 3D object upright orientation estimation using 3D Convolutional Networks (ConvNets), and the method is designed in the style of divide-and-conquer ...

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for linear second-order elliptic reactiondiffusion-advection equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the extension of the error analysis of the hpDGFEM to the case when anisotropic (shape-irregular) elements and anisotropic polynomial degrees are used. ...