The efficient parallel solution to large sparse linear systems of equations Ax = b is a central issue in many numerical computations in science and engineering. In fact, the solution of linear systems of equations is frequently the most time-consuming phase of several simulation codes with the development of efficient parallel algorithms virtually mandatory to permit the large scale computations required in recent applications. Iterative methods based on Krylov subspaces are particularly attractive to parallel computers provided an effective preconditioning technique is available. Computing and applying an effective preconditioner on a parallel machine is often the most decisive and difficult task to be carried out. Sparse approximate inverses are conceptually parallel in nature, as they provide an explicit approximation of A^−1 which can be applied to a vector by a matrix-by-vector product only. This family of preconditioners have been in depth investigated in recent years and many different variants are presently available in literature. In the present review, the most noticeable advancements in this field will be addressed with a short description of the algorithms and a discussion on the strong and weak points of each approximate inverse variant.

Approximate inverse preconditioning for the solution of large sparse linear systems

JANNA, CARLO;FERRONATO, MASSIMILIANO;GAMBOLATI, GIUSEPPE
2013

Abstract

The efficient parallel solution to large sparse linear systems of equations Ax = b is a central issue in many numerical computations in science and engineering. In fact, the solution of linear systems of equations is frequently the most time-consuming phase of several simulation codes with the development of efficient parallel algorithms virtually mandatory to permit the large scale computations required in recent applications. Iterative methods based on Krylov subspaces are particularly attractive to parallel computers provided an effective preconditioning technique is available. Computing and applying an effective preconditioner on a parallel machine is often the most decisive and difficult task to be carried out. Sparse approximate inverses are conceptually parallel in nature, as they provide an explicit approximation of A^−1 which can be applied to a vector by a matrix-by-vector product only. This family of preconditioners have been in depth investigated in recent years and many different variants are presently available in literature. In the present review, the most noticeable advancements in this field will be addressed with a short description of the algorithms and a discussion on the strong and weak points of each approximate inverse variant.
2013
Computational Technology Review
9781874672616
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/2572950
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact