SplitNewton 0.1.1

Split Newton Solver

SplitNewton

Unbounded SPLIT Newton with pseudo-transient continuation and backtracking

Good for ill-conditioned problems where there are two different sets of systems

Particular applications include

• Fast-Slow Reaction-Diffusion systems
• CFD - Pressure-Velocity coupling

How to install and execute?

Just run

pip install splitnewton

There is an examples folder that contains a test function and driver program

How good is this?

Consider the test problem

$\lambda_{a} = 10^{6}$, $\lambda_{b} = 10^{2}$

and the second system $\lambda_{c} = 10^{-1}$ $\lambda_{d} = 10^{-4}$

$$ u' = 0.25 * \begin{bmatrix} \lambda_a & \dots & 0 & 0 & \dots & 0 \newline \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \newline 0 & \dots & \lambda_b & 0 & \dots & 0 \newline 0 & \dots & 0 & \lambda_c & \dots & 0 \newline \vdots & \ddots & \vdots & \vdots & \ddots & \vdots \newline 0 & \dots & 0 & 0 & \dots & \lambda_d \end{bmatrix} u^{4} $$

For N=5000 (with no backtracking and pseudo-transient continuation),

Method	Time	Iterations
Split Newton	9 seconds	32
Newton	not converged > 1 min	NA

Whom to contact?

Please direct your queries to gpavanb1 for any questions.