Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems

We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into m× m× m subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to m . The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with m^6 while the number of iterations increases only proportionally to √(m) . Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems.