hypre-ILU

The hypre-ILU solver is a parallel ILU solver based on a domain decomposition framework. It may be use iteratively as a standalone solver or smoother, as well as a preconditioner for accelerators like Krylov subspace methods. This solver implements various parallel variants of the dual threshold (truncation) incomplete LU factorization - ILUT, and the level-based incomplete LU factorization - ILUk.

Overview

The parallel hypre-ILU solver follows a domain decomposition approach for solving distributed sparse linear systems of equations. The strategy is to decompose the domain into interior and interface nodes, where an interface node separates two interior nodes from adjacent domains. In the purely algebraic setting, this is equivalent to partitioning the matrix row data into local (processor-owned) data and external (off-processor-owned) data. The resulting global view of the partitioned matrix has (diagonal) blocks corresponding to local data, and off-diagonal blocks corresponding to non-local data. The resulting parallel ILU strategy is composed of a (local) block factorization and a (global) Schur complement solve. Several strategies provided to efficiently solve the Schur complement system.

The following represents a minimal set of functions, and some optional functions, to call to use the hypre_ILU solver. For simplicity, we ignore the function parameters here, and refer the reader to the reference manual for more details on the parameters and their defaults.

  • HYPRE_ILUCreate: Create the hypre_ILU solver object.

  • HYPRE_ILUSetType: Set the type of ILU factorization to do. Here, the user specifies one of several flavors of parallel ILU based on the different combinations of local factorizations and global Schur complement solves. Please refer to the reference manual for more details about the different options available to the user.

  • (Optional) HYPRE_ILUSetLevelOfFill: Set the level of fill used by the level-based ILUk strategy.

  • (Optional) HYPRE_ILUSetSchurMaxIter: Set the maximum number of iterations for solving the Schur complement system.

  • (Optional) HYPRE_ILUSetMaxIter: Set the maximum number of iterations when used as a solver or smoother.

  • HYPRE_ILUSetup: Setup and hypre_ILU solver object.

  • HYPRE_ILUSolve: Solve the linear system.

  • HYPRE_ILUDestroy: Destroy the hypre_ILU solver object

For more details about additional solver options and parameters, please refer to the reference manual. NOTE: The hypre_ILU solver is currently only supported by the IJ interface.