03-1. Solver Settings

In this section we will discuss the input file solver/settings.input. This file sets parameters for the solver and domain of the simulation. This the file is read in by the subroutine read_me in the reader.f90 module. The relevant inputs extracted from this file are then shared with the rest of the code.

We will refer to the equations:

$\frac{\partial u }{\partial t} = \epsilon \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial x^2} \right) + F(u,v)\\ \frac{\partial v }{\partial t}= \left(\frac{\partial^2 v}{\partial x^2}+ \frac{\partial^2 v}{\partial y^2} \right) + G(u,v),$

Explanation of File Contents

This first section is:

Settings ________________
1           !!! Time_switch (time marching if 1)
1           !!! Non_Linear_switch (non linear if 1)
2           !!! Eqn_number
2           !!! Domain_number

Time_switch toggles the the solver between a BVP solver when set to 0 and a IBVP solver when set to 1. When we have a BVP, this is equivalent to setting the time derivatives $\frac{\partial u}{\partial t} = 1$ and $\frac{\partial v}{\partial t} = 1$ .
Non_Linear_switch controls the Newton-iteration solver, disabling it when set to 0 and enabling it when set to 1. The equation that we solve when the Non_Linear_switch is 0 is linear, and so $F(u,v) = G(u,v) =0.$
Eqn_number sets how many equations to solve. If set to 1, we only solve for $u$ . If set to 2, we solve for both $u$ and $v$ .
Domain_number specifies the number of domains. If set to 1, we only solve over one domain $x$ . If set to 2, we only solve over one domain $x$ and $y$ .

Domain sections:

!!! xdomain settings_____
30        !!! nx - size of x domain
0,5   !!! xl, xr - start and end points of x domain
0,2.25    !!! x_stretch_on or off, grid stretch parameter (xhalf)

!!! ydomain settings_____
30        !!! ny - size of y domain
0,5       !!! yl, yr - start and end points of y domain
0,2.25    !!! y_stretch_on or off, grid stretch parameter (yhalf)

!!! temporal marching settings_____
1000              !!! nt - size of t domain
0.d0,10.d0        !!! tl, tr - start and end points of time domain

Here we set the sizes of the domains.

nx, ny and nt set the number of points inside each domain.
xl and xr are the start and end of the $x$ domain respectively. This is repeated for $y$ and $t$ .
For the spatial domains $x$ and $y$ we also include a grid stretch switch x_stretch_on and y_stretch_on When set to 0, then we have uniform domains. When set to 1, half the grid points have been clustered between xl and xhalf in a smooth manner. This is the same for $y$ .

!!! general settings_____
4           !!! DiffOrder - order of finite differences scheme
1.d-6       !!! Newton_Error
2000        !!! Max_iter - max Newton iterations

DiffOrder sets the order of the finite differences. Can be 2 (second order), $3$ (fourth order interior and second order boundaries) or $4$ (fourth order).
Newton_Error sets the tolerance needed to achieve convergence in the non-linear Newton iteration at each step. A smaller number yields a more accurate result.
Max_iter sets the maximum number of iterations allowed for the non-liner Newton iteration. If we pass this number, convergence is not reached and the solver stops.