FSPAI

Factorized Sparse Approximate Inverses

This is a dummy textLatest release is 1.0

We developed a sequential and highly scalable parallel C/C++ implementation of the
known FSPAI (Factorized SParse Approximate Inverses) algorithm.

Theory

FSPAI is a preconditioner for large sparse and ill-conditioned symmetric positive
definite systems of linear equations. It is the factorized version of the SPAI
algorithm. FSPAI is inherently parallel and generates a preconditioner which approximates the inverse of the cholesky factor of the system matrix, i.e.,

/home/sedlacek/Fspai.pdf

Based on an initial chosen sparsity structure, FSPAI automatically updates its
sparsity structure and improves an a current approximation.

Implementation and Features

• Single source providing
  • highly scalable parallel implementation
  • sequential (MPI free) implementation
• Support for real and complex valued problems
• PCG solver available using HYPRE package
• Written in C/C++

We are currently working on a next release which will cover a highly scalable
block version of FSPAI, i.e., BFSPAI.

Some References

Papers

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Further

• Short summary on sparse approximate inverses with core reference list: summary.pdf
• Extended reference list: extended.pdf

Authors

• Thomas Huckle
• Matous Sedlacek

License

FSPAI: Factorized Sparse Approximate Inverses
Copyright © 2010-2011, Matous Sedlacek
Research Unit Scientific Computing in Computer Science - Informatics V
Technische Universität München

This program is free software: you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program. If not, see http://www.gnu.org/licenses/.

If you obtain any results with FSPAI we would appreciate that you refer to FSPAI.

Further work on Sparse Approximate Inverses

• SPAI: Parallel Implementation on SPAI — Sparse Approximate Inverses:
  http://www.computational.unibas.ch/software/spai/
• MSPAI: Parallel implementation of MSPAI — Modified Sparse Approximate Inverses:
  http://www5.in.tum.de/wiki/index.php/MSPAI
• PARASAILS: Parallel Sparse Approximate Inverse (Least-Squares) Preconditioner:
  https://computation.llnl.gov/casc/parasails/parasails.html
• HYPRE: Software on high performance preconditioners containing a PARASAILS module:
  https://computation.llnl.gov/casc/linear_solvers/sls_hypre.html