The HTFETI Method Variant Gluing Cluster Subdomains by Kernel Matrices Representing the Rigid Body Motions

The proposed algorithm called the Hybrid Total Finite Element Tearing and Interconnecting method (HTFETI) is a variant of the TFETI domain decomposition method suitable for large-scale problems with hundreds of thousands of subdomains. The floating subdomains are gathered into several groups belonging to individual clusters. We use the new idea consisting in gluing the cluster subdomains using kernel matrices defined by the rigid body motions. This technique reduces the size of the coarse problem. While the size of the coarse problem depends linearly on the number of subdomains in the classical TFETI method, it depends linearly on the number of clusters in the HTFETI method. The zero weighted averages across the interfaces of neighbouring subdomains (an alternative to the constraints enforcing the continuity across the corners used, e.g., in the FETI-DP method) improve conditioning of the resulting system of linear equations.