A framework for parallel adaptive finite element methods and its template based implementation in C++

Abstract

Finite element meshes are large, richly structured sets whose internal relationships must be visible to different parts of a finite element program. This causes software engineerings problems that increase when adaptive mesh refinement and multilevel preconditioners are applied. Even more problems arise when finite element methods have to be implemented for parallel computers since the meshes have to be mapped onto the hardware topology so that their locality is preserved. We have designed a framework for parallel adaptive finite element methods that centers upon a problem-oriented index scheme as a new high level description method for finite element meshes. Within the index scheme, important mesh relations can be expressed by simple algebraic operations in {ie105-1}. We give an overview of the indexing methodology and outline the main parts of the framework. Special emphasis is on the reuse of several C++ template libraries—including standard container classes and the library for data parallel programming of the Promoter programming model.