Notebook Tutorials

📜 Extensive user guide, mostly based on step-by-step tutorials …

All tutorials are written in jupyter notebooks, that can be :

• read using the online documentation

• downloaded from the notebook folder and played with

🛠️ Basic usage tutorials are finalized and polished, the rest is still in construction …

Notebooks are categorized into those main sections :

1. Basic usage : how to generate and use basic \(Q\)-coefficients and \(Q_\Delta\) approximations, through a step-by-step tutorial going from generic Runge-Kutta methods to SDC for simple problems.

2. Extended usage : additional features or qmat (\(S\)-matrix, hCoeffs, dTau coefficients, …) to go deeper into SDC

3. Components usage : how to use the main utility modules, like qmat.lagrange, etc …

Base usage

📜 From Butcher Tables to Spectral Deferred Corrections

• Step 1 : generate \(Q\)-coefficients
• Step 2 : build a Runge-Kutta type time-stepper
• Step 3 : generate \(Q_\Delta\) coefficients
• Step 4 : build a Spectral Deferred Correction type time-stepper
• Step 5 : residuals of SDC sweeps

Extended usage

📜 Going deeper into SDC’s understanding

• Advanced Step 1 : Zero-to-Nodes (Z2N) and Node-to-Node (N2N)
• Advanced Step 2 : generalizing the prolongation for RK-type and SDC-type time-steppers
• Advanced Step 3 : generalizing the initialization of SDC-type time-steppers

Components usage

📜 How to use the utility modules

• Tutorial 1 : using the qmat.lagrange module
• Tutorial 2 : using the qmat.nodes module