Macro Element Formulations for Recursive Domain Decomposition in h-p Adaptive Finite Element Analysis

A novel technique for spatial discretization domain decomposition, for h-p adaptive finite element analysis (AFEA), is developed and investigated. The method is fully recursive, and it is based on a generalized family of "macro elements" designed for hierarchal AFEA implementations. The new macro elements are derived to model evolving sub-domain patches of the full analysis space, by incorporating the local governing differential equations into the parameterization of the macro element definition. Each macro element is, effectively, custom-designed and custom-refined through the AFEA process to meet the needs of the sub-domain discretization model, at each adaptive step. Basic electromagnetic problems are tested, and the benefits and costs of using these decompositions in concurrent processing environments are assessed