Ecosyste.ms: Awesome
An open API service indexing awesome lists of open source software.
https://github.com/jipolanco/BSplineKit.jl
A collection of B-spline tools in Julia
https://github.com/jipolanco/BSplineKit.jl
b-splines basis-recombination collocation function-approximation galerkin interpolation julia splines
Last synced: 3 months ago
JSON representation
A collection of B-spline tools in Julia
- Host: GitHub
- URL: https://github.com/jipolanco/BSplineKit.jl
- Owner: jipolanco
- License: mit
- Created: 2020-04-29T17:05:47.000Z (over 4 years ago)
- Default Branch: master
- Last Pushed: 2024-07-09T12:30:12.000Z (4 months ago)
- Last Synced: 2024-07-10T11:04:07.411Z (4 months ago)
- Topics: b-splines, basis-recombination, collocation, function-approximation, galerkin, interpolation, julia, splines
- Language: Julia
- Homepage: https://jipolanco.github.io/BSplineKit.jl/dev/
- Size: 5.41 MB
- Stars: 50
- Watchers: 4
- Forks: 9
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
- Citation: CITATION.cff
Awesome Lists containing this project
- awesome-sciml - jipolanco/BSplineKit.jl: A collection of B-spline tools in Julia
README
# BSplineKit.jl
[](https://jipolanco.github.io/BSplineKit.jl/stable/)
[](https://jipolanco.github.io/BSplineKit.jl/dev/)
[](https://doi.org/10.5281/zenodo.5150350)
[](https://github.com/jipolanco/BSplineKit.jl/actions)
[](https://codecov.io/gh/jipolanco/BSplineKit.jl)
Tools for B-spline based Galerkin and collocation methods in Julia.
## Features
This package provides:
- B-spline bases of arbitrary order on uniform and non-uniform grids;
- evaluation of splines and their derivatives and integrals;
- spline interpolations and function approximation;
- basis recombination, for generating bases satisfying homogeneous boundary
conditions using linear combinations of B-splines.
Supported boundary conditions include Dirichlet, Neumann, Robin, and
generalisations of these;
- banded Galerkin and collocation matrices for solving differential equations,
using B-spline and recombined bases;
- efficient "banded" 3D arrays as an extension of banded matrices.
These can store 3D tensors associated to quadratic terms in Galerkin methods.
## Example usage
The following is a very brief overview of some of the functionality provided
by this package.
- Interpolate discrete data using cubic splines (B-spline order `k = 4`):
```julia
xdata = (0:10).^2 # points don't need to be uniformly distributed
ydata = rand(length(xdata))
itp = interpolate(xdata, ydata, BSplineOrder(4))
itp(12.3) # interpolation can be evaluated at any intermediate point
```
- Create B-spline basis of order `k = 6` (polynomial degree 5) from a given
set of breakpoints:
```julia
breaks = log2.(1:16) # breakpoints don't need to be uniformly distributed either
B = BSplineBasis(BSplineOrder(6), breaks)
```
- Approximate known function by a spline in a previously constructed basis:
```julia
f(x) = exp(-x) * sin(x)
fapprox = approximate(f, B)
f(2.3), fapprox(2.3) # (0.07476354233090601, 0.0747642348243861)
```
- Create derived basis satisfying homogeneous [Robin boundary
conditions](https://en.wikipedia.org/wiki/Robin_boundary_condition) on the
two boundaries:
```julia
bc = Derivative(0) + 3Derivative(1)
R = RecombinedBSplineBasis(B, bc) # satisfies u ∓ 3u' = 0 on the left/right boundary
```
- Construct [mass matrix](https://en.wikipedia.org/wiki/Mass_matrix) and
[stiffness matrix](https://en.wikipedia.org/wiki/Stiffness_matrix) for
the Galerkin method in the recombined basis:
```julia
# By default, M and L are Hermitian banded matrices
M = galerkin_matrix(R)
L = galerkin_matrix(R, (Derivative(1), Derivative(1)))
```
- Construct banded 3D tensor associated to non-linear term of the [Burgers
equation](https://en.wikipedia.org/wiki/Burgers%27_equation):
```julia
T = galerkin_tensor(R, (Derivative(0), Derivative(1), Derivative(0)))
```
See the [heat equation
example](https://jipolanco.github.io/BSplineKit.jl/stable/generated/heat/) in
the docs for the use of these tools to solve partial differential equations.
## References
- C. de Boor, *A Practical Guide to Splines*. New York: Springer-Verlag, 1978.
- J. P. Boyd, *Chebyshev and Fourier Spectral Methods*, Second Edition.
Mineola, N.Y: Dover Publications, 2001.
- O. Botella and K. Shariff, *B-spline Methods in Fluid Dynamics*, Int. J. Comput.
Fluid Dyn. 17, 133 (2003).