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

Abstract

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. Here, we demonstrate that this approach is effective for example problems in Poisson’s equation, nonlinear elasticity, and thermomechanical elastoplasticity.

Authors:
ORCiD logo [1];  [2];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Univ. of California, Los Angeles, CA (United States)
  3. Rensselaer Polytechnic Inst., Troy, NY (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Army
OSTI Identifier:
1595011
Report Number(s):
SAND-2019-14363J
Journal ID: ISSN 0177-0667; 682699
Grant/Contract Number:  
AC04-94AL85000; SC00066117; NA0003525; W911NF1410301; W911NF16C0117
Resource Type:
Accepted Manuscript
Journal Name:
Engineering with Computers
Additional Journal Information:
Journal Volume: 36; Journal ID: ISSN 0177-0667
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Automated; Adjoint; A posteriori; Error estimation; Adaptation; Finite element

Citation Formats

Granzow, Brian N., Oberai, Assad A., and Shephard, Mark S. An automated approach for parallel adjoint-based error estimation and mesh adaptation. United States: N. p., 2019. Web. doi:10.1007/s00366-019-00890-2.
Granzow, Brian N., Oberai, Assad A., & Shephard, Mark S. An automated approach for parallel adjoint-based error estimation and mesh adaptation. United States. doi:https://doi.org/10.1007/s00366-019-00890-2
Granzow, Brian N., Oberai, Assad A., and Shephard, Mark S. Wed . "An automated approach for parallel adjoint-based error estimation and mesh adaptation". United States. doi:https://doi.org/10.1007/s00366-019-00890-2. https://www.osti.gov/servlets/purl/1595011.
@article{osti_1595011,
title = {An automated approach for parallel adjoint-based error estimation and mesh adaptation},
author = {Granzow, Brian N. and Oberai, Assad A. and Shephard, Mark S.},
abstractNote = {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. Here, we demonstrate that this approach is effective for example problems in Poisson’s equation, nonlinear elasticity, and thermomechanical elastoplasticity.},
doi = {10.1007/s00366-019-00890-2},
journal = {Engineering with Computers},
number = ,
volume = 36,
place = {United States},
year = {2019},
month = {12}
}

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