SNLS -- small non-linear solver library

 ________  ________   ___       ________      
|\   ____\|\   ___  \|\  \     |\   ____\     
\ \  \___|\ \  \\ \  \ \  \    \ \  \___|_    
 \ \_____  \ \  \\ \  \ \  \    \ \_____  \   
  \|____|\  \ \  \\ \  \ \  \____\|____|\  \  
    ____\_\  \ \__\\ \__\ \_______\____\_\  \ 
   |\_________\|__| \|__|\|_______|\_________\
   \|_________|                   \|_________|

BACKGROUND

SNLS (small non-linear solver) is a C++ library for solving non-linear systems of equations. The emphasis is on small systems of equations for which direct factorization of the Jacobian is appropriate. The systems of equations may be numerically ill-conditioned. Implementation is amenable to GPU usage, with the idea that class instantiation would occur within device functions for non-batch type solvers.

Examples of work that has made use of SNLS or substantially equivalent algorithms:

• Journal publication on use with a porosity mechanics type model
• Journal publication on use with a crystal mechanics type model

Solvers currently in the library:

• SNLSTrDlDenseG Dogleg approximation to the trust-region sub-problem for multi-dimensional nonlinear systems of equations. This method reduces to a Newton-Raphson approach near the solution. These methods are sometimes described as "restricted step" approaches instead of trust-region approaches. See, for example, Practical Methods of Optimization. As compared to general trust-region approaches in scalar minimization, the approach here for solving non-linear systems amounts to assuming that the Hessian matrix can be approximated using information from the Jacobian of the system.
• SNLSHybrdTrDLDenseG A hybrid trust region type solver, dogleg approximation for dense general Jacobian matrix that makes use of a rank-1 update of the jacobian using QR factorization. The method is inspired by SNLS current trust region dogleg solver and Powell's original hybrid method for nonlinear equations, and MINPACK's modified version of it. Powell's original hybrid method can be found at: M. J. D. Powell, "A hybrid method for nonlinear equations", in Numerical methods for nonlinear algebraic equations. MINPACK's user guide is found at https://doi.org/10.2172/6997568 . As compared to general trust-region approaches in scalar minimization, the approach here for solving non-linear systems amounts to assuming that the Hessian matrix can be approximated using information from the Jacobian of the system.
• SNLSTrDlDenseG_Batch a batch version of SNLSTrDlDenseG that is only available if the library is compiled with the -DUSE_BATCH_SOLVERS=On cmake option. It makes use of the RAJA Performance Suite to abstract away the complexity of memory management and execution strategies of forall loops. The test/SNLS_batch_testdriver.cc provides an example of how this solver, the memory manager, and forall abstraction layer can be used to solve a modified Broyden Tridiagonal Problem.
• NewtonBB Simple 1D Newton solver with a fallback to bisection. If the zero of the function can be bounded then this solver can return a result even if the function is badly behaved.

BUILDING

The build system is cmake-based.

Dependencies:

• blt -- required
  • https://github.com/LLNL/blt
  • in cmake invocation specify location with -DBLT_SOURCE_DIR

TESTING

Run cmake with -DENABLE_TESTS=ON and do make test

DEVELOPMENT

The develop branch is the main development branch for snls. Changes to develop are by pull request.

AUTHORS

The principal devleoper of SNLS is Nathan Barton, nrbarton@llnl.gov. Brett Wayne and Robert Carson have also made contributions.

CITATION

SNLS may be cited using the following bibtex entry:

@Misc{snls,
title = {SNLS},
author = {Wayne, Brett M. and Barton, Nathan R. and USDOE National Nuclear Security Administration},
abstractNote = {{SNLS} (small non-linear solver) is a C++ library for solving non-linear systems. The emphasis is on small systems of equations for which direct factorization of the Jacobian is appropriate. The systems of equations may be numerically ill-conditioned. Implementation is amenable to {GPU} usage, with the idea that class instantiation would occur within device functions.},
doi = {10.11578/dc.20181217.9},
year = 2018,
month = {9},
url = {https://github.com/LLNL/SNLS},
annote =    {
   https://www.osti.gov//servlets/purl/1487196
   https://www.osti.gov/biblio/1487196
}
}

LICENSE

License is under the BSD-3-Clause license. See LICENSE file for details. And see also the NOTICE file.

SPDX-License-Identifier: BSD-3-Clause

LLNL-CODE-761139