A Blocked Incomplete Cholesky Preconditioner for Hierarchical-memory Computers

We develop a drop-threshold incomplete Cholesky preconditioner which uses blocked data structures and computational kernels for improved performance on computers with one or more levels of cache memory. The techniques are similar to those used for Cholesky factorization in sparse direct solvers. We report on the performance of our preconditioned conjugate gradient solver on sparse linear systems from three application areas: structural mechanics, image analysis and materials modeling. On average, our blocked implementation (block-size 8) results in a speedup of over two.