ashao/newton-krylov_ooc

An Out-of-Core Newton-Krylov Solver

Out-of-Core Newton-Krylov Solver

Documentation

https://newton-krylov-ooc.readthedocs.io/

Background

A Newton-Krylov (NK) solver is a nested iterative solver for approximating the solution of a system of equations. An application in the realm of time-dependent ordinary or partial differential equations is to find an initial condition such that the solution of the differential equations, with that initial condition, is cyclo-stationary (periodic) solution in time.

Each iteration of a NK solver requires the evaluation of the function being solved for. For large systems of equations, this evaluation can take hours of wall-clock time on a supercomputer, and may require utilizing a batch job submission system. Typical implementations of NK solvers are in-core. They have a driver program that stays resident in memory while function evaluations occur. In some computing environments, it is impractical, or forbidden, to have such a driver program reside in memory for the amount of time needed for multiple function evaluations. A primary goal of the NK solver implemented in this repository is to avoid this in-core requirement.

High-level Solver Description

The solver tracks solver-state, which includes a list of steps that the solver has completed and computational results of the solver. The solver-state is saved to a file whenever the solver-state is updated. The solver has a resume option. When specified, the solver reads in a previously saved solver-state and skips previously completed steps. When function evaluation invokes a long running batch job, the solver exits after the job is submitted, and the batch job is augmented to invoke the solver with the resume option specified. This implementation effectively enables the solver to resume where it left off, and avoids the requirement for the solver to remain resident in memory.

Directory Hierarchy Sketch

.
├── baselines                   # directories containing baselines that travis tests
│   ├── travis_long_dye_decay   # are compared to
│   ├── travis_long_iage
│   └── travis_short
├── docs                        # solver documentation
│   └── source
├── input
│   ├── cime_pop                # cime_pop model specific input files
│   └── test_problem            # test_problem model specific input files
├── notebooks                   # jupyter notebooks utilizing the solver
├── scripts                     # non-python scripts, model independent
├── src                         # model independent python code
│   ├── cime_pop                # cime_pop model specific python code
│   └── test_problem            # test_problem model specific python code
└── tests                       # pytest tests