Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

Victor M. Calo, David Pardo, Maciej R. Paszyński

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

In this paper we present a goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and a parallel multi-frontal direct solver. The algorithm automatically generates (without any user interaction) a sequence of meshes delivering exponential convergence of a prescribed quantity of interest with respect to the number of degrees of freedom. The sequence of meshes is generated from a given initial mesh, by performing h (breaking elements into smaller elements), p (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal-oriented adaptivity and the solver work fully in parallel. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. We apply the methodology described to the three-dimensional simulation of the borehole resistivity measurement of direct current through casing in the presence of invasion.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages1485-1495
Number of pages11
DOIs
StatePublished - May 22 2011

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