# SplitFXM
[](https://pepy.tech/project/splitfxm)
[](https://doi.org/10.5281/zenodo.13882261)
1D [Finite-Difference](https://en.wikipedia.org/wiki/Finite_difference_method) or [Finite-Volume](https://en.wikipedia.org/wiki/Finite_volume_method) using asymmetric stencils with [adaptive mesh refinement](https://en.wikipedia.org/wiki/Adaptive_mesh_refinement) and steady-state solver using Newton and [Split-Newton](https://github.com/gpavanb1/SplitNewton) approach
## What does 'split' mean?
The system is divided into two and for ease of communication, let's refer to first set of variables as "outer" and the second as "inner".
* Holding the outer variables fixed, Newton iteration is performed till convergence using the sub-Jacobian
* One Newton step is performed for the outer variables with inner held fixed (using its sub-Jacobian)
* This process is repeated till convergence criterion is met for the full system (same as in Newton)
## How to install and execute?
Just run
```
pip install splitfxm
```
There is an [examples](https://github.com/gpavanb1/SplitFXM/models) folder that contains a test model - [Advection-Diffusion](https://en.wikipedia.org/wiki/Convection%E2%80%93diffusion_equation)
You can define your own equations by simply creating a derived class from `Model` and adding to the `_equations` using existing or custom equations!
A basic driver program is as follows
```
from splitfxm.domain import Domain
from splitfxm.simulation import Simulation
from splitfxm.schemes import default_scheme
from splitfxm.visualize import draw
# Define the problem
method = 'FDM'
m = AdvectionDiffusion(c=0.2, nu=0.001, method=method)
d = Domain.from_size(20, 1, 1, ["u", "v", "w"]) # nx, nb_left, nb_right, variables
ics = {"u": "gaussian", "v": "rarefaction", "w": "tophat"}
bcs = {
"u": {
"left": "periodic",
"right": "periodic"
},
"v": {
"left": {"dirichlet": 3},
"right": {"dirichlet": 4}
},
"w": {
"left": {"dirichlet": 2},
"right": "periodic"
}
}
s = Simulation(d, m, ics, bcs, default_scheme(method))
# Advance in time or to steady state
s.evolve(t_diff=0.1)
bounds = [[-1., -2., 0.], [5., 4., 3.]]
iter = s.steady_state(split=True, split_loc=1, bounds=bounds)
# Visualize
draw(d, "label")
```
## How to build from source?
Since v0.4.0, SplitFXM utilizes Cython for accelerated computation. To build from source, you will need to install Cython and run the following command:
```
python setup.py build_ext --inplace
```
## Run benchmark
There is a benchmark that is included, which compares the time it takes to generate both a sparse and dense Jacobian. The results are as follows:
For N=250,
| Method | Time |
|-----------|------------|
| Dense | 20 seconds |
| Sparse | ~0.6 seconds |
The benchmark can be executed from the parent folder using the command
`python -m pytest -s benchmark`
## How to run tests?
To run the tests, execute the following command from the parent folder:
```
python -m pytest tests
```
You can use the `-s` flag to show `print` outputs of the tests
## How to get coverage?
To get coverage, execute the following command from the parent folder:
```
python -m pytest --cov=splitfxm --cov-report <option> tests
```
The `option` can be related to showing covered/missed lines or specifying the output format of the report. For example, to get a line-by-line report, use the following command:
```
python -m pytest --cov=splitfxm --cov-report term-missing tests
```
## Whom to contact?
Please direct your queries to [gpavanb1](http://github.com/gpavanb1)
for any questions.
## Acknowledgements
Special thanks to [Cantera](https://github.com/Cantera/cantera) and [WENO-Scalar](https://github.com/comp-physics/WENO-scalar) for serving as an inspiration for code architecture.
## Citing
If you are using `SplitFXM` in any scientific work, please make sure to cite as follows
```
@software{pavan_b_govindaraju_2024_13882261,
author = {Pavan B Govindaraju},
title = {gpavanb1/SplitFXM: v0.4.0},
month = oct,
year = 2024,
publisher = {Zenodo},
version = {v0.4.0},
doi = {10.5281/zenodo.13882261},
url = {https://doi.org/10.5281/zenodo.13882261}
}
```
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