Grid systems have evolved over time from traditional grid computing to service grids. Grid computing focuses on high perfomance computing, based on the concepts of cluster-building and resource sharing, by which grid systems are able to solve dataand comptutationally intensive tasks. Service grids include additionally virtualized, application field-specific services, providing for geographicall...

I I of Partial A general survey of grid generation is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for such meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split LvetWee~; structured grids and unstructured meshes. A...

An approach to solve nite time horizon sub-optimal feedback control problems for partial di erential equations is proposed by solving dynamic programming equations on adaptive sparse grids. The approach is illustrated for the wave equation and an extension to equations of Schrödinger type is indicated. A semi-discrete optimal control problem is introduced and the feedback control is derived fro...

This work concerns the development of an adaptive multi-solver approach for CFD simulation of viscous flows. Curvilinear grids are used near solid bodies to capture boundary layers, and stuctured adaptive Cartesian grids are used away from the body to fill the majority of the computational domain. An edge-based meshless scheme is used in the interface region to connnect the near-body and off-bo...

We devise and study experimentally adaptive strategies driven by a posteriori error estimates to select automatically both the space mesh and the polynomial degree in the numerical approximation of diffusion equations in two space dimensions. The adaptation is based on equilibrated flux estimates. These estimates are presented here for inhomogeneous Dirichlet and Neumann boundary conditions, fo...

Polynomial approximations of computationally intensive models are central to uncertainty quantification. This paper describes an adaptive method for nonintrusive pseudospectral approximation, based on Smolyak’s algorithm with generalized sparse grids. We rigorously analyze and extend the nonadaptive method proposed in [P. G. Constantine, M. S. Eldred, and E. T. Phipps, Comput. Methods Appl. Mec...

In this paper we analyze the problem of adaptivity for one-step numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating grids of minimal computational cost for which the local error is below a prescribed tolerance (optimal grids). The grids are generated by introducing an auxiliary independent variable τ and finding a grid deformation map, t = Θ(τ), that maps an equidi...

The temperature fields inside a collapsing bubble near a plane rigid wall are investigated. We develop a numerical method based on the boundary element method combined with the finite volume method. In this method, the adaptive unstructured grids which are generated by Delaunay triangulation are used inside the largely deformable bubble to consider the heat transfer of the internal gas. We comp...

Adaptive mesh refinement (AMR) is a numerical simulation technique used in computational fluid dynamics (CFD). By using a set of nested grids of different resolutions, AMR combines the simplicity of structured rectilinear grids with the ability to adapt to local changes in complexity in the domain. Without proper interpolation on the boundaries of grids of different levels of a hierarchy, disco...

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (MICI) in two dimensions. MICI is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a hig...