qmat 0.0.5

Generation of Q-coefficients for Spectral Deferred Corrections (and other time-integration methods ...)

QMat Package

qmat is a python package to generate matrix coefficients related to Collocation methods, Spectral Deferred Corrections (SDC), and more general multi-stages time-integration methods (like Runge-Kutta, etc ...).

It allows to generate $Q$-coefficients for multi-stages methods (equivalent to Butcher tables) :

$$ Q\text{-coefficients : } \begin{array}{c|c} \tau & Q \ \hline & w^\top \end{array} \quad \Leftrightarrow \quad \begin{array}{c|c} c & A \ \hline & b^\top \end{array} \quad\text{(Butcher table)} $$

and many different lower-triangular approximation of the $Q$ matrix, named $Q_\Delta$, which are key elements for Spectral Deferred Correction (SDC), or more general Iterated Runge-Kutta Methods.

Installation

🛠️ Still in construction, only installation from source is enable yet, see current instructions ...

Basic usage

📜 If you are already familiar with those concepts, you can use this package like this :

from qmat import genQCoeffs, genQDeltaCoeffs

# Coefficients or specific collocation method
nodes, weights, Q = genQCoeffs("Collocation", nNodes=4, nodeType="LEGENDRE", quadType="RADAU-RIGHT")

# QDelta matrix from Implicit-Euler based SDC
QDelta = genQDeltaCoeffs("IE", nodes=nodes)

# Butcher table of the classical explicit RK4 method
c, b, A = genQCoeffs("ERK4")

🔔 If you are not familiar with SDC or related methods, and want to learn more about it, checkout the latest documentation build and in particular the step by step tutorials

For any contribution, please checkout out (very cool) Contribution Guidelines