BLOCK ILU PRECONDITIONERS FOR PARALLEL AMR/C SIMULATIONS

Abstract. In this work we study the behavior of Block ILU preconditioners in distribuited-memory parallel simulations. Of particulat interest is the resulting preconditioned iterative solver behavior when adaptive mesh refinement and coarsening (AMR/C) are utilized. Here, we use a domain decomposition scheme to partition the spatial domain as a collection of subdo-mains. These subdomains are repartitioned dynamically when the mesh adaptation proceeds. To build approximate preconditioners, we employ the Block-Jacobi and Additive Schwarz tech-niques. In both cases, incomplete LU factorizations (ILU) are applied as local preconditioners. In addition to this, the Reverse Cuthill-McKee (RCM) and Quotient Minimum Degree (QMD) reodering algorithms are applied in the local ILU preconditioners. Numerical studies are con-ducted using the object oriented AMR/C software system libMesh linked to the PETSc solver library in order to compare the efficiency of Block ILU preconditioners. Preliminary results suggest that Block-Jacobi preconditioners have lower computation cost than Additive Schwarz