We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in comput...

The multiscale multigrid method is presented in this article to solve the linear systems arising from a fourth order discretisation. We used a symbolic algebra packageMathematica to derive a family of finite difference approximations on a 27 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at selected grid points. A set of test problems are presente...

Recent developments in strategies and software tools for overset structured grid generation and domain connectivity are described. A scripting approach based on a library of grid generation script macros is adopted to speed up the grid generation process. Advances in this method involve the development of high level functions that encapsulate more complex grid generation tasks. Sample applicati...

Stencil-based kernels constitute the core of many scientific applications on block-structured grids. Unfortunately, these codes achieve a low fraction of peak performance. In this paper, we demonstrate one method for automatically generating high-quality stencil code. First, we perform a search over various instruction-level optimizations to find the best platform-specific combination. These op...

This paper discusses compact-stencil nite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and ef ciency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also disc...

We present a new smoothness indicator that evaluates the local smoothness of a function inside of a stencil. The corresponding weighted essentially non-oscillatory (WENO) finite difference scheme can provide the fifth convergence order in smooth regions. The proposed WENO scheme provides at least the same or improved behavior over the classical fifth-order WENO scheme [9] and other fifth-order ...

High fidelity numerical simulation of compressible flow requires the method being used to have both stable shock-capturing capability and high spectral resolution. Recently, a family Targeted Essentially Non-Oscillatory (TENO) schemes is developed fulfill such requirements. Although TENO has very low dissipation for smooth flow, it introduces cutoff value CT maintain non-oscillatory property. A...

In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm, and the second version corresponds to a slightly modified version of the same. In conjugate gradient method to solve partial differential equations, matrix ...

204 words) We have developed a novel method to derive scale information from quasi-stationary images, which relies on a rotation-guided multi-scale analysis of features derived from Gray Level Co-occurrence Matrices (GLCM). Unlike other methods for multi-scale texture characterization, our method does not require rotation-invariant textural features, but instead uses orientation information der...