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Section: Software

Keywords : multilevel method, domain decomposition, schur complement, parallel iterative solver.

HIPS

Participants : Jérémie Gaidamour, Pascal Hénon [ corresponding member ] , Jean Roman, Yousef Saad.

HIPS (Hierarchical Iterative Parallel Solver) is a scientific library that provides an efficient parallel iterative solver for very large sparse linear systems.

HIPS has been built on top of the PHIDAL library; it is based on the ordering and partitioning that were developed in PHIDAL and it proposes some new hybrid direct iterative algorithms.

The keypoint of the methods implemented in HIPS is to defined an ordering and a partition of the unknowns that relies on a form of nested dissection ordering in which cross points in the separators play a special role (Hierarchical Interface Decomposition ordering). The subgraphs obtained by the nested dissection correspond to the unknowns that are eliminated using a direct method and the Schur complement system on the remaining of the unknowns (that correspond to the interface between the subgraphs viewed as subdomains) is solved using an iterative method (GMRES or Conjugate Gradient at the time being).

This special ordering and partitioning allow the use of dense block algorithms both in the direct and iterative part of the solver and provides a high degree of parallelism to these algorithms.

We propose several algorithmic variants to solve the Schur complement system that can be adapted to the geometry of the problem: typically some strategies are more suitable for systems coming from a 2D problem discretization and others for a 3D problem; the choice of the method also depends on the numerical difficulty of the problem. Thus HIPS is a generic library that provides several methods to build an efficient preconditioner in many of these situations. It handles symmetric, unsymmetric, real or complex matrices. It also provides the scalar preconditioner based on the multistage ILUT factorization that were developed in PHIDAL . HIPS has been downloaded as a private project on InriaGForge and will be released in the next year.


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