Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

Abstract

This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar approach allows obtaining a linear computational cost of adaptive mesh transformations and computations performed over refined meshes. The computations are done by a hyper-graph grammar driven algorithm applicable to three-dimensional problems. For the case of typical refinements performed towards a point or an edge, the algorithm yields linear computational cost with respect to the mesh nodes for its sequential execution and logarithmic cost for its parallel execution. Such hyper-graph grammar productions are the mathematical formalism used to describe the computational algorithm implementing the finite element method. Each production indicates the smallest atomic task that can be executed concurrently. The mesh transformations and computations by using the hyper-graph grammar-based approach have been tested in the GALOIS environment. We conclude the paper with some numerical results performed on a shared-memory Linux cluster node, for the case of three-dimensional computational meshes refined towards a point, an edge and a face.

A Collaborative Design System of Distributed Computing Mode Based on Node Adaptive Algorithm

“…After researching and analyzing the defects of Hadoop in the laboratory, researchers designed Spark with better stability and performance. Compared with Hadoop, Spark's biggest improvement is to use Resilient Distributed Dataset (RDD) to solve the problem of excessive I/O, and it is also compatible with the Map Reduce model in the Hadoop framework [14][15]. At present, Spark has publicly disclosed the interface information and the complete deployment method.…”