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Title: Off-diagonal Jacobian support for Nodal BCs

Abstract

In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \normal" assembly has taken place, and eciently replace the contents of those rows with the contributions associ- ated to the nodal boundary conditions. 2. An interface for allowing users to specify both the residual and Jacobian contributions associated to their nonlinear boundary condition.

Authors:
 [1];  [1];  [1];  [1];  [1]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1178371
Report Number(s):
INL/EXT-15-34246
DOE Contract Number:
AC07-05ID14517
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; jacobian; MOOSE

Citation Formats

Peterson, John W., Andrs, David, Gaston, Derek R., Permann, Cody J., and Slaughter, Andrew E. Off-diagonal Jacobian support for Nodal BCs. United States: N. p., 2015. Web. doi:10.2172/1178371.
Peterson, John W., Andrs, David, Gaston, Derek R., Permann, Cody J., & Slaughter, Andrew E. Off-diagonal Jacobian support for Nodal BCs. United States. doi:10.2172/1178371.
Peterson, John W., Andrs, David, Gaston, Derek R., Permann, Cody J., and Slaughter, Andrew E. Thu . "Off-diagonal Jacobian support for Nodal BCs". United States. doi:10.2172/1178371. https://www.osti.gov/servlets/purl/1178371.
@article{osti_1178371,
title = {Off-diagonal Jacobian support for Nodal BCs},
author = {Peterson, John W. and Andrs, David and Gaston, Derek R. and Permann, Cody J. and Slaughter, Andrew E.},
abstractNote = {In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \normal" assembly has taken place, and eciently replace the contents of those rows with the contributions associ- ated to the nodal boundary conditions. 2. An interface for allowing users to specify both the residual and Jacobian contributions associated to their nonlinear boundary condition.},
doi = {10.2172/1178371},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}

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