Equal Subcycled to Non-Subcycled Region Ratio of 1:1

We first test subcycling on an equal distribution of non-subcycled and subcycled nodes, i.e. a region ratio of , with $7896$ nodes, $15256$ edges and $8700$ volumetric elements. Selecting a random node ahead of the initial notch, we plot its nodal displacements in Figure 4.2 for the various subcycling parameters. From this figure we can see that subcycled solutions are very close to the reference solution, although their accuracies decrease with an increasing subcycling parameter.

The timing results for the internal and cohesive force subroutines, the main loop and the overall solution are presented in Table 4.5. As expected, the time for the internal force calculations decreases as the subcycling parameter grows, although for ${\it m} = 4$, the cost resulting from the cohesive forces and main solution loop offsets the savings of the internal forces - a $11\%$ loss.

Figure 4.2: Nodal displacements of a random node ahead of the notch for a problem with an equal region ratio () with subcycling parameters of ${\it m} = 1, 4, 10, 16$ and $20$.

Table 4.1: Timing results (in $s$) for a problem with an equal region ratio () with subcycling parameters of ${\it m} = 1, 4, 10, 16$ and $20$.

Subroutine	Reference Case [s], m = 1	m = 4	m = 10	m = 16	m = 20
$R^\textrm{co}$	424.13	628.72	503.81	479.24	469.56
$R^\textrm{in}$	733.89	472.52	300.37	256.66	238.05
$Main$	427.29	652.91	499.89	469.59	439.78
$Total$	1628.54	1811.59	1359.70	1259.68	1201.80
$\%$ $Total$ $Savings$		-11%	17%	23%	26%