Offdiagonal Jacobian support for Nodal BCs
Abstract
In this brief note, we describe the implementation of odiagonal 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 odiagonal 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:
 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/EXT1534246
 DOE Contract Number:
 AC0705ID14517
 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.. Offdiagonal 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.. Offdiagonal 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.. 2015.
"Offdiagonal Jacobian support for Nodal BCs". United States.
doi:10.2172/1178371. https://www.osti.gov/servlets/purl/1178371.
@article{osti_1178371,
title = {Offdiagonal 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 odiagonal 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 odiagonal 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 = 2015,
month = 1
}

EPISODEB is a package of eight subroutines for the numerical solution of the initial value problem for systems of first order ordinary differential equations whose Jacobian matrices are banded or can be approximated by band matrices. The package can be used for either stiff or nonstiff systems whose Jacobians can be approximated by band matrices. It is especially suited to problems with intermittent highspeed transients or waves.IBM360,370; FORTRAN IV; OS/360,370; 102K bytes are used to execute the doubleprecision version of the sample problem.

Future developments in stiff integration techniques: stability of methods that do not use an exact Jacobian
Although there are many open theoretical questions for stiff (and nonstiff) variableorder, variablestep methods, it seems unlikely that there will be any major computational advances as far as integration methods for the general nonlinear problem. The major drawback of many of the methods that have been proposed in the last few years is that they involve too many matrix operations, or operations on larger matrices than in some of the more straightforward techniques, such as the backward differentiation formulas. However, advances in techniques for handling large, sparse matrices may affect the choice of integration method for very large problems. Thismore » 
New insights into input relegation control for inverse kinematics of a redundant manipulator. Part 1, On the orthogonality of matrices B and J and comparison to the extended Jacobian method
A method for kinematically modeling a constrained rigid body mechanical system and a method for controlling such a system termed input relegation control (IRC) were applied to resolve the kinematic redundancy of a serial link manipulator moving in an open chain configuration in. A set of equations was introduced to define a new vector variable parameterizing the redundant degrees of freedom (DOF) as a linear function of the joint velocities. The new set was combined with the classical kinematic velocity model of manipulator and solved to yield a well specified solution for the joint velocities as a function of themore » 
JFKengine: A Jacobian and Forward Kinematics Generator
During robot path planning and control the equations that describe the robot motions are determined and solved. Historically these expressions were derived analytically offline. For robots that must adapt to their environment or perform a wide range of tasks, a way is needed to rapidly rederive these expressions to take into account the robot kinematic changes, such as when a tool is added to the endeffector. The JFKengine software was developed to automatically produce the expressions representing the manipulator arm motion, including the manipulator arm Jacobian and the forward kinematic expressions. Its programming interface can be used in conjunction withmore »