Parallel Structured Adaptive Mesh Refinement

Abstract

Parallel structured adaptive mesh refinement is a technique for efficient utilization of computational resources. It reduces the computational effort and memory requirements needed for numerical simulation of complex phenomena, described by partial differential equations. Structured adaptive mesh refinement (SAMR) is applied in simulations where the domain is divided into logically rectangular patches, where each patch is discretized with a structured mesh. The purpose of adaptive mesh refinement is to automatically adapt the mesh to the resolution required to represent important features of the simulated phenomenon in different subdomains. In a parallel computing context, an important consequence of the adaptation is that the dynamically changing resolution leads to a dynamically changing work load, data volume, and communication pattern at run-time. This calls for dynamic load balancing and has implications for data placement as well as parallelization granularity.This chapter gives an overview of structured adaptive mesh refinement approaches. After a brief introductory survey of SAMR techniques and software packages, the main part of the chapter addresses various issues related to implementation of SAMR on parallel computers. In particular programming models, data placement and load balancing are discussed, for shared memory as well as distributed memory platforms. Various approaches and algorithms are presented. The appropriate choice of dynamic load balancing algorithm, data placement strategy, programming model, etc., depends on both the application state and the computer platform. There

Stable Difference Methods for Block-Oriented Adaptive Grids

“…In this class of methods, the computational domain is decomposed into a hierarchy of non-overlapping grid blocks, where refinement is undertaken with respect to entire grid blocks only. In comparison with the method of Berger-Colella, the overhead associated with grid management is reduced and load balancing becomes a simpler and more straightforward task [22]. There are two strategies available for block refinement.…”

Stability at Nonconforming Grid Interfaces for a High Order Discretization of the Schrödinger Equation

“…In the block-structured approach, refinement is carried out concurrently for all points in a, typically rectangular, grid patch if the numerical solution fails to meet a user-defined local error tolerance. In order for such an approach to be successful, the artificial internal boundaries between adjoining grid blocks with different grid densities need to be treated carefully so as to preserve stability and accuracy properties [3]. In this paper we consider the numerical properties across nonconforming grid blocks (for which collocation points across grid boundaries do not match) for a finite difference discretization of the Schrödinger equation.…”

Data structures and algorithms for high-dimensional structured adaptive mesh refinement

“…In order to construct a practical refinement scheme that works well even in higher dimensions, the framework presented in this paper is built on a structured block-based refinement strategy [1] allowing blocks to be refined anisotropically. The mesh nodes and their mutual relationships are maintained in a kd-tree [6].…”

“…Structured adaptive mesh refinement (SAMR) is an active area of research within the scientific computing community [1]. By adjusting the resolution of the computational mesh dynamically to features in the solution or the computational domain, widely varying scales of resolution can be represented simultaneously.…”