An automated approach for parallel adjoint-based error estimation and mesh adaptation

  • Brian N. GranzowEmail author
  • Assad A. Oberai
  • Mark S. Shephard
Original Article


In finite element simulations, not all of the data are of equal importance. In fact, the primary purpose of a numerical study is often to accurately assess only one or two engineering output quantities that can be expressed as functionals. Adjoint-based error estimation provides a means to approximate the discretization error in functional quantities and mesh adaptation provides the ability to control this discretization error by locally modifying the finite element mesh. In the past, adjoint-based error estimation has only been accessible to expert practitioners in the field of solid mechanics. In this work, we present an approach to automate the process of adjoint-based error estimation and mesh adaptation on parallel machines. This process is intended to lower the barrier of entry to adjoint-based error estimation and mesh adaptation for solid mechanics practitioners. We demonstrate that this approach is effective for example problems in Poisson’s equation, nonlinear elasticity, and thermomechanical elastoplasticity.


Automated Adjoint A posteriori Error estimation Adaptation Finite element 



The authors acknowledge the support of IBM Corporation in the performance of this research. The computing resources of the Center for Computational Innovations at Rensselaer Polytechnic Institute are also acknowledged. The development of tools used in this work was partly supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under award DE-SC00066117 (FASTMath SciDAC Institute). The authors would like to thank Li Dong for providing the discrete geometric model used for the microglial cell example and Max Bloomfield for the geometric model used for the solder ball example.

This work was performed at the time at Rensselaer Polytechnic Institute before the authors moved to different organizations. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

This work is supported by the U.S. Army grants W911NF1410301 and W911NF16C0117.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Sandia National LaboratoriesAlbuquerqueUSA
  2. 2.Scientific Computation Research CenterRensselaer Polytechnic InstituteTroyUSA
  3. 3.Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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