At a practical level you may be looking for parallel ways to use PETSc's native (but serial) ILU. The simplest parallel extension is processor-block Jacobi which applies ILU on the processor-owned degrees of freedom but with no overlap: -pc_type bjacobi -sub_pc_type ilu The overlapping version is with ASM: -pc_type asm -sub_pc_type ilu where -pc_asm_overlap controls the overlap distance. Finally one can use the serial ILU as a smoother in geometric multigrid, for example in combination with overlapping ASM: -pc_type mg -mg_levels_pc_type asm -mg_levels_sub_pc_type ilu Apologies if this was all assumed to be known in your original question. Indeed, application of parallel direct solvers in PETSc often uses hyper/mumps/superlu, though I'm not familiar with ILU in these packages. Ed Dear Professor,

I'm writing about this mail about the ILU algorithm in PETSc. I have noticed that the ILU in PETSs cannot be paralleled, and the Hypre providing the parallel implement of ILU. My questions is : why the PETSc does not provide the parallel implement of ILU directly, instead of linking to the Hypre to obtain the Parallel ILU algorithm? PS: the attachment is the Parallel ILU algorithm in Hypre. I'm looking forward to hear you! Best, Gang Chen Sichuan Univertsity, School of Mathematics, Chengdu, China

-- Ed Bueler Dept of Mathematics and Statistics University of Alaska Fairbanks Fairbanks, AK 99775-6660 306C Chapman