A parallel adaptive block FSAI preconditioner for finite elements geomechanical models

Efficient ad hoc preconditioners are a key factor for a successful implementation of linear solvers in a parallel computing environment. The class of Factorized Sparse Approximate Inverses (FSAI), although originally developed for scalar machines has proven extremely promising in multicore hardware. A recent evolution of FSAI is Block FSAI (BFSAI) which clusters the largest coefficients of the preconditioned matrix in a number of diagonal blocks defined in advance. A further improvement of BFSAI is the adaptive BFSAI (labelled ABF) where the non zero pattern of the BFSAI preconditioner is not prescribed a priori but computed automatically and adaptively by a suitable algorithm. Numerical results from large finite element (FE) geomechanical models show that ABF coupled with an incomplete Cholesky factorization of each individual block, i.e. ABF-IC, may outperform BFSAI-IC by up to a factor 4 while exhibiting an excellent degree of parallelization on any multiprocessor computer.