Parallel self-adaptive hp finite element method with shared data structure

Maciej Paszyński¹ , David Pardo²

¹Department of Computer Science, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland.
²Departamento de Matemática Aplicada, Estadística e Investigación Operativa, UPV/EHU, Campus de Leioa, Vizcaya, and IKERBASQUE (Basque Foundation for Sciences), Bilbao, Spain.

DOI:

https://doi.org/10.7494/cmms.2011.2.0361

Abstract:

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), 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 present details of the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. The presentation is enriched by numerical results of the 3D DC borehole resistivity measurement simulations.

Cite as:

Paszyński, M., & Pardo, D. (2011). Parallel self-adaptive hp finite element method with shared data structure. Computer Methods in Materials Science, 11(2), 399 – 405. https://doi.org/10.7494/cmms.2011.2.0361

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