1 Parallel Iterative Solvers with the Selective Blocking Preconditioning for Simulations of Fault-Zone Contact

Iterative solver with preconditioning is the most powerful choice for large-scale scientific com-putation, especially for the parallel computing. In nonlinear problems such as contact simulations for geophysics, the condition numbers of the coefficient matrices are usually large due to special constraint conditions. The result is slow convergence of the iterative solver. In this study, a new preconditioning method, called selective blocking was developed along with special partitioning method for parallel computing on the GeoFEM platform. For symmetric matrices, block incomplete Cholesky factorization without inter-block fill-in, using selective blocking (SB-BIC(0)) shows excellent performance, memory efficiency and robustness. SB-BIC(0) remains stable for a wide range of penalty number values, while the per-formance of BIC(1) or BIC(2) declines according to the penalty number. It is also shown that the partitioning method for elimination of edge-cuts in contact groups improves convergence of par-allel iterative solvers with localized preconditioning. This newly developed method provides ro-bust and smooth convergence in 3D solid mechanics simulations for geophysics with contact conditions performed on a Hitachi SR2201 parallel computer with 128 processing elements. In the next stage, we are implementing these newly developed preconditioning methods into the linear solvers of the GeoFEM platform and are going to solve larger-scale, realistic contact problems with friction using many processors