An Irregular Meshless h-p Adaptive Finite Element Analysis Formulation for High Performance Computing Environments

A new meshless finite element analysis formulation is developed and investigated. The approach is based on a hybrid coupling of conventional meshless theory, and the "irregular-cut" finite element technique. The method 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 naturally suited for high performance computing environments, and has been developed and implemented for h-p adaptive finite element analysis applications in practical electromagnetics, on the CLUMEQ Supercomputer Centre facilities at McGill University. Computational results based on 2-D and 3-D benchmark analyses support the correctness of the formulation, and demonstrate the computational performance and efficiency of the implementation