An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects
An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as nonproportional damping such that the time integration of the scheme is provably stable with a critical time step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.
 Authors:

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 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL652798
Journal ID: ISSN 00295981
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 International Journal for Numerical Methods in Engineering
 Additional Journal Information:
 Journal Volume: 104; Journal Issue: 7; Journal ID: ISSN 00295981
 Publisher:
 Wiley
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; embedded mesh; Lagrange multipliers; ALE method
 OSTI Identifier:
 1377784
Puso, M. A., Kokko, E., Settgast, R., Sanders, J., Simpkins, B., and Liu, B.. An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects. United States: N. p.,
Web. doi:10.1002/nme.4796.
Puso, M. A., Kokko, E., Settgast, R., Sanders, J., Simpkins, B., & Liu, B.. An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects. United States. doi:10.1002/nme.4796.
Puso, M. A., Kokko, E., Settgast, R., Sanders, J., Simpkins, B., and Liu, B.. 2014.
"An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects". United States.
doi:10.1002/nme.4796. https://www.osti.gov/servlets/purl/1377784.
@article{osti_1377784,
title = {An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects},
author = {Puso, M. A. and Kokko, E. and Settgast, R. and Sanders, J. and Simpkins, B. and Liu, B.},
abstractNote = {An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as nonproportional damping such that the time integration of the scheme is provably stable with a critical time step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.},
doi = {10.1002/nme.4796},
journal = {International Journal for Numerical Methods in Engineering},
number = 7,
volume = 104,
place = {United States},
year = {2014},
month = {10}
}