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Figure 1.1-1: Domain geometry and interface position

v3.04.321 SSLV321 - Validation of XFEM preconditioning for a grazing interface#

Summary:

This test validates the pre-conditioner dedicated to quadratic XFEM elements. The problem corresponds to that of a 3D block cut by an interface XFEM. Multiaxial compression is applied over the entire surface of the block, including on interface XFEM. The expected analytical solution is a \({P}_{1}\) move within the domain. This solution is captured naturally by the elements \({P}_{1}\) and \({P}_{2}\) of Code_Aster.

As the interface passes near the mesh nodes, the conditioning of the stiffness matrix increases [1,2]. The usual strategies, used in Code_Aster (readjusting the interface to the nodes and eliminating ddls Heaviside), based on « estimative » criteria, are not always adapted to control the conditioning and the precision of the results [2]. These disadvantages are all the more penalizing, with quadratic elements.

The new strategy (construction of a diagonal preconditioner by blocks) makes it possible to overcome all these disadvantages [3].

This test includes 5 models:

  • \(A\): a HEXA8 \(\mathrm{3D}\) modeling with an interface XFEM of equation \(x+y+z+0.01\mathrm{=}0\)

  • \(B\): a HEXA20 \(\mathrm{3D}\) modeling with an interface XFEM of equation \(x+y+z+0.1=0\)

  • \(C\): a HEXA20 \(\mathrm{3D}\) modeling with an interface XFEM of equation \(x+y+z+0.01\mathrm{=}0\)

  • \(D\): a HEXA8 \(\mathrm{3D}\) modeling with an interface XFEM of equation \(x+y+z+0.011=0\)

  • \(E\): a HEXA8 \(\mathrm{3D}\) modeling with an interface XFEM of equation \(x+y+z+0.011=0\)