A Parallel Meshless Formulation for $h$ -$p$ Adaptive Finite Element Analysis

A novel parallel formulation for meshless adaptive finite element analysis is developed and investigated. The method is based on an integrated interpretation of conventional meshless theory and the generalized irregular-cut formulation for triangles and tetrahedra. The new formulation provides a near orthogonal hierarchal relationship among local basis functions, and supports the virtually unrestricted introduction and refinement of localized modeling degrees of freedom in a discretization. The formulation is intended for h-p adaptive refinements, and is well suited to high-performance parallel and distributed computing implementations. Initial test implementations have been purpose-built to investigate the main issues and performance characteristics of adaptive finite element analysis applications in electromagnetics, for large-scale computations on the CLUMEQ Supercomputer Centre facilities at McGill University, Montreal, QC, Canada. Numerical results based on 1-D, 2-D, and 3-D benchmark analyses verify the correctness of the new formulation and illustrate the potential performance of the implementations.