[CIG-SHORT] XFEM

[Ehsan Haghighat]

This is not hard to see (and can be found in Ethan Coon's Columbia thesis which is online). If you have a discontinuity which almost lines
up with a cell edge, then you generate an ill-conditioned system. This behavior is ubiquitous.

Oh, I now see what you mean by singularity. Yes, that becomes singular with standard integral scheme as the Jacobian of sub-trinagles used for xfem integration approaches zero (and as a result, cartesian derivatives of basis functions become ill-conditioned). However, Sukumar has addressed this issue long time ago (2004-2005). A work around was the use of sub-cells that would automatically ignores small Jacobians.
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