https://github.com/maroba/numgrids
Working with numerical grids made easy.
https://github.com/maroba/numgrids
numerical-methods scientific-computing spectral-methods
Last synced: about 1 year ago
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Working with numerical grids made easy.
- Host: GitHub
- URL: https://github.com/maroba/numgrids
- Owner: maroba
- License: mit
- Created: 2022-07-29T14:03:14.000Z (almost 4 years ago)
- Default Branch: main
- Last Pushed: 2023-07-07T13:45:07.000Z (almost 3 years ago)
- Last Synced: 2025-04-14T21:32:28.525Z (about 1 year ago)
- Topics: numerical-methods, scientific-computing, spectral-methods
- Language: Python
- Homepage:
- Size: 1.18 MB
- Stars: 10
- Watchers: 1
- Forks: 1
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
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README
numgrids
Working with numerical grids made easy.
**Main Features**
- Quickly define numerical grids for any rectangular or curvilinear coordinate system
- Differentiation and integration
- Interpolation
- Easy manipulation of meshed functions
- Using high precision spectral methods (FFT + Chebyshev) wherever possible
- Includes multigrid functionality
- Fully compatible with *numpy*
## Installation
```shell
pip install --upgrade numgrids
```
## Quick Start
As a quick example, here is how you define a grid on the unit disk using polar coordinates.
Along the azimuthal (angular) direction, choose an equidistant spacing with periodic boundary conditions:
```python
from numgrids import *
from numpy import pi
axis_phi = Axis(AxisType.EQUIDISTANT, 50, 0, 2*pi, periodic=True)
```
Along the radial axis, let's choose a non-equidistant spacing:
```python
axis_radial = Axis(AxisType.CHEBYSHEV, 20, 0, 1)
```
Now combine the axes to a **grid**:
```python
grid = Grid(axis_radial, axis_phi)
```
**Sample** a meshed function on this grid:
```python
from numpy import exp, sin
R, Phi = grid.meshed_coords
f = R**2 * sin(Phi)**2
```
Define **partial derivatives** $\partial/\partial r$ and $\partial/\partial \varphi$ and apply them:
```python
# second argument means derivative order, third argument means axis index:
d_dr = Diff(grid, 1, 0)
d_dphi = Diff(grid, 1, 1)
df_dr = d_dr(f)
df_dphi = d_dphi(f)
```
Obtain the **matrix representation** of the differential operators:
```python
d_dr.as_matrix()
Out: <1000x1000 sparse matrix of type ''
with 20000 stored elements in COOrdinate format>
```
Define **integration operator**
$$
\int \dots dr d\varphi
$$
```python
I = Integral(grid)
```
Calculate the area integral
$$
\int f(r, \varphi) r dr d\varphi
$$
(taking into account the appropriate integration measure $r$ for polar coordinates):
```python
I(f * R)
```
Setting **boundary** values to zero
```python
f[grid.boundary] = 0 # grid.boundary is boolean mask selecting boundary grid points
```
or to something more complicated:
```python
f[grid.boundary] = exp(-R[grid.boundary])
```
Create an **interpolation function**
```python
inter = Interpolator(grid, f)
```
Interpolate for a single point
```python
point = (0.1, 0.5)
inter(point)
```
or for many points at once, like for a parametrized curve:
```python
t = np.linspace(0, 1, 100)
points = zip(2*t, t**2)
inter(points)
```
## Usage / Example Notebooks
To get an idea how *numgrids* can be used, have a look at the following example notebooks:
- [How to define grids](examples/how-to-define-grids.ipynb)
- [Partial derivatives in any dimension](examples/partial-derivatives.ipynb)
- [Polar coordinates on unit disk](examples/polar-cooordinates-on-unit-disk.ipynb)
- [Spherical Grid and the Spherical Laplacian](examples/spherical-grid.ipynb)
- [Solving the Schrödinger equation for the quantum harmonic oscillator](examples/quantum-harmonic-oscillator.ipynb)
## Development
### Setting up the project
Clone the repository
```
git clone https://github.com/maroba/numgrids.git
```
In the project root directory, submit
```
python setup.py develop
```
to install the package in development mode.
Run the tests:
```
python -m unittest discover tests
```
### Contributing
1. Fork the repository
2. Develop
3. Write tests!
4. Create an [issue](https://github.com/maroba/numgrids/issues)
5. Create a pull request, when done