online read us now
Paper details
Number 3 - September 2018
Volume 28 - 2018
Applications of a hyper-graph grammar system in adaptive finite-element computations
Piotr Gurgul, Konrad Jopek, Keshav Pingali, Anna Paszyńska
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.
Keywords
adaptive finite element method, hyper-graph grammars, mesh-based computations