Parallel Multilevel Block ILU Preconditioning Techniques for Large Sparse Linear Systems
نویسندگان
چکیده
We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU) factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different block independent set algorithms and different coarse level solution strategies. We also use some diagonal thresholding and perturbation strategies to enhance factorization stability. Numerical experiments indicate that our parallel multilevel block ILU preconditioners are robust and efficient.
منابع مشابه
Parallel two level block ILU preconditioning techniques for solving large sparse linear systems
We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct loca...
متن کاملDistributed block independent set algorithms and parallel multilevel ILU preconditioners
We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent sets (BISs). Two algorithms for constructing BISs of a sparse matrix in a distributed environment are proposed. We compare a few implementations o...
متن کاملPreconditioning Techniques for Large LinearSystems: A Survey
This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An e...
متن کاملA Multi-Level Preconditioner with Applications to the Numerical Simulation of Coating Problems
A multi-level preconditioned iterative method based on a multi-level block ILU factoriza-tion preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coef-cient matrices usually have several rows with zero diagonal values that may cause stability diiculty in standard ILU factoriza...
متن کاملPii: S0168-9274(99)00047-1
We investigate the use of sparse approximate inverse techniques in a multilevel block ILU preconditioner to design a robust and efficient parallelizable preconditioner for solving general sparse matrices. The resulting preconditioner retains robustness of the multilevel block ILU preconditioner (BILUM) and offers a convenient means to control the fill-in elements when large size blocks (subdoma...
متن کامل