This paper is concerned with the treatment of higher order multi-grid techniques for obtaining accurate finite difference approximations to partial differential equations. The three basic techniques considered are a multi-grid process involving smoothing via higher order difference approximations, iterated defect corrections with multi-grid used as an inner loop equation solver, and tau-extrapo...

In the first part of the paper, we introduce an overlapping mortar finite element method for solving two-dimensional elliptic problems discretized on overlapping nonmatching grids. We prove an optimal error bound and estimate the condition numbers of certain overlapping Schwarz preconditioned systems for the two-subdomain case. We show that the error bound is independent of the size of the over...

A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and (adaptive) hier...

A novel system for depth estimation is proposed with the use of Symbiotic Genetic Algorithms for the continuous problem of disparity surface approximation. The approach is based on the decomposition of the entire surface to very small non-overlapping patches described by low-order bivariate polynomials and the use of symbiotic optimisation to enforce smoothness at the boundaries of these patche...

The cluster based on the density is a kind of cluster analysis, its main merit is to discover cluster of arbitrary shape and insensitive to the noise data. R-tree organizes the space index according to the spatial data, the spatial overlapping is in a big way, the inquiry efficiency is low, in order to adapt the need of massive GIS inquiry application, this paper firstly carries on the division...

A global multi-grid/GMRES solution methodology on distributed memory machines is successfully developed in this study. To preserve the effectiveness of the multigrid scheme, the grid partitioning is based on the communication graph of the coarsest grid, so that all levels of the multi-grids are located in the same zone (processor). Each node of the graph is weighted with the total number of the...

The multi-band microstrip antennas are realized by cutting more than one slots at an appropriate position inside the patch or by placing the open circuit stub on the edges of the patch or by using the combination of slots and stub. In this paper, an analysis to study the multi-band response in stub loaded two half U-slot cut rectangular microstrip antenna is presented. The first half U-slot in ...

The application of Reinforcement Learning (RL) algorithms to learn tasks for robots is often limited by the large dimension of the state space, which may make prohibitive its application on a tabular model. In this paper, we introduce LEAP (Learning Entities Adaptive Partitioning), a model-free learning algorithm that uses overlapping partitions which are dynamically modified to learn near-opti...

Previous research has reported that attention to color afterimages speeds up their decay. However, the inducing stimuli in these studies have been overlapping, thereby implying that they involved overlapping receptive fields of the responsible neurons. As a result it is difficult to interpret the effect of focusing attention on a phenomenally projected target-afterimage. Here, we present a meth...