A collection of spectral collocation differentiation matrices

This collection is based on their original matlab/octave version developed by Weidemann and Reddy and available from DMSUITE. The theory and examples are explained in their paper: J. A. C. Weidemann and S. C. Reddy, A MATLAB Differentiation Matrix Suite, ACM Transactions on Mathematical Software, 26, (2000): 465-519.

The port to python was initiated as part of a larger project by ronojoy as https://github.com/ronojoy/pyddx.git

It is available on PyPI. You can install and update dmsuite with the following command:

python3 -m pip install --user -U dmsuite

Some examples are available in the examples directory. Considering for example the case of Chebyshev differentiation matrix, it is first setup by:

cheb = Chebyshev(degree=NCHEB)

with NCHEB the degree of polynomials considered. The differentiation matrices of degree 1 and 2 are obtained as:

D1 = cheb.at_order(1)
D2 = cheb.at_order(2)

and so on for larger orders of differentiation. The colocation nodes are stored in cheb.nodes which can used to compute a any function at these location, e.g.::

y = np.sin(2 * pi * cheb.nodes)

First and second order differentiation are then simply obtained as D1 @ y and D2 @ y, respectively. For more complex uses, e.g. to compute eigenvectors and eigenvalues of partial differential equations refer to

• Labrosse, S., Morison, A., Deguen, R., and Alboussière, T. Rayleigh-Bénard convection in a creeping solid with a phase change at either or both horizontal boundaries. J. Fluid Mech., 846:5–36, 2018.
• Morison, A., Labrosse, S., Deguen, R., and Alboussière, T. Timescale of overturn in a magma ocean cumulate. Earth Planet. Sci. Lett., 516:25 – 36, 2019.