Keywords: domain decomposition, FETI, parallel implementation, PETSc, contact problem.

problem to a smaller dual, relatively well conditioned strictly convex iteratively solved QP problem but also transforms the general inequality constraints into the nonnegativity constraints so that efficient algorithms that exploit inexpensive projections and other tools may be exploited. The Total-FETI-1 (TFETI-1) simplifies the inversion of stiffness matrices of subdomains by using Lagrange multipliers not only for gluing the subdomains along the auxiliary interfaces, but also for implementation of the Dirichlet boundary conditions. This method may be even more efficient than the original FETI-1.

Our research concerns the development of the scalable FETI-based methods for contact problems combining the FETI approach with algorithms for bound constrained QP problems with a known rate of convergence given in terms of the spectral condition number (QPMPGP, SMALBE) and their testing in a parallel environment. The most difficult part, solution of subdomain problems, may be usually carried out in parallel without any coordination, so that high parallel scalability is enjoyed. The increasing number of subdomains decreases the subdomain problem size resulting in shorter time for subdomain stiffness matrix factorizations and subsequently forward and backward substitutions during pseudoinverse application, but on the other hand the increasing number of subdomains assuming a fixed discretization parameter increases the dual dimension and the coarse problem size resulting in a longer time for all dual vector operations and orthogonal projector applications.

This paper deals with the analysis of three types of parallelization strategies for TFETI-1 for contact problems. The data distributions and implementations of the most relevant actions using PETSc functions are discussed. The numerical results presented confirm high parallel scalability of the solution of subdomain problems (Cholesky factorization of subdomain stiffness matrices and the pseudoinverse matrix by vector multiplication) and also a high level of parallel scalability of computation of the distributed coarse problem matrix having orthonormal rows.

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