Parallel Self-Adaptive hp Finite Element Method Algorithm with Shared Data Structure

In this paper we present a new parallel algorithm of the self-adaptive hp Finite Element Method (hp-FEM) with shared data structures. The algorithm generates in a fully automatic mode (without any user interaction) a sequence of meshes delivering exponential convergence of the prescribed quantity of interest with respect to the mesh size (number of degrees of freedom). The sequence of meshes is generated from the prescribed initial mesh, by performing h (breaking elements into smaller elements) or p (adjusting polynomial orders of approximation) or hp (both) refinements on selected finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp adaptivity and the solver, work fully in parallel. We will present details of the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. The presentation will be enriched by numerical results of the problem of 3D AC/DC borehole resistivity measurement simulations.