Parallel simulations of 3 d DC borehole resistivity measurements with goal - oriented self - adaptive hp finite element method

In this paper we present a parallel algorithm of the goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and with parallel multi-frontal direct solver. 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), 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. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. The presentation is enriched by numerical simulation of the problem of through casing 3D DC borehole resistivity measurement simulations in presence of invasion.