Approximate Cyclic Reduction Multilevel Preconditioner for General SparseMatrices

摘要

We discuss an iterative method for solving large sparse systems of equations. Ahybrid method is introduced which uses ideas both from ILU preconditioning from multigrid. The resulting preconditioning technique requires the matrix only. A multilevel structure is obtained by using maximal independent sets for graph coarsening. For Schur complement approximation on coarser graphs, an incomplete Gaussian elimination is used. The resulting preconditioner has a transparant modular structure similar to the algorithmic structure of a multigrid V-cycle.