7. Summaries of results

We can compare the paths given by the four methods (simplex, upwind, upwind& FMM and geometric):

The four methods all give the same propagation path, which is very similar to the experimental data ().

It is possible to compare the calculation time for the same number of propagation steps (13) of the four methods. For the simplex and upwind methods, performance was checked using the computation domain restriction. It should be noted that the restriction of the domain makes it possible to greatly reduce the calculation time of these two methods and to make the performance of the mesh, simplex and upwind methods comparable.

Mesh	Method	Time (s)
quadrangles	Meshing	19.0
	Simplexe	13.0
	Upwind	16
	Geometric	15.3

The results make it possible to validate on a simple case the calculation of stress intensity factors in \(I\) mode for the \(\text{X-FEM}\) elements for the various methods.