Factorized Sparse Approximate Inverses

This is a dummy textLatest release is 1.1

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

Note that there is a scalable implementation of Modified Sparse Approximate
Inverses (MSPAI) as well.

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.,

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

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
Arbitrary start patterns, i.e., possibility to compute a FSAI without
updating the pattern
Support for sparse methods using CXSparse by Tim Davis
Caching and Hashing approach to avoid redundant Cholesky decompositions
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.

Download

FSPAI 1.1

In contrast to FSPAI 1.0, FSPAI 1.1 additionally requires CXSparse and UFconfig.
If you are not going to use the Fspai Caching/Hashing or the sparse methods,
you can use FSPAI 1.0 instead.

Source code tar ball: fspai-1.1.tar.gz.
Manual: fspai-1.1.pdf.
Only the HTML documentation of source code: htmlonly-fspai-1.1.tar.gz

FSPAI 1.0

Source code tar ball: fspai-1.0.tar.gz.
Manual: fspai-1.0.pdf.
Only the HTML documentation of source code: htmlonly-fspai-1.0.tar.gz

Tested environments

Shaheen from the KAUST Supercomputing Laboratory (KSL) at King
Abdullah University of Science and Technology (KAUST):
- 65536 compute cores: 16 racks of Blue Gene/P, each containing
  1024 quad-core, 32-bit 850 MHz PowerPC compute nodes
- Architecture: PowerPC (PPC)
- Compiler version: IBM XL C/C++ Advanced Edition for Blue Gene/P, V9.0
- Libraries:
  - Lapack 3.2.1
  - MPI based on MPICH2
  - HYPRE 2.7

InfiniBand-Cluster of the Lehrstuhl Rechnertechnik und Rechnerorganisation/
Parallelrechnerarchitektur of Technische Universtität München:
- 128 compute cores: AMD Opteron™ Processor 850
- Architecture: x86_64
- Compiler version: gcc version 4.2.4 (Ubuntu 4.2.4-1ubuntu3)
- Libraries:
  - Lapack 3.0
  - MPI based on MPICH 1.2.7
  - HYPRE 2.7.0b

i686-pc-linux-gnu:
- Processor: Intel® Core™2 Duo CPU P8700 @ 2.53GHz
- Architecture: i686
- Compiler version: gcc version 4.3.4 (Gentoo 4.3.4 p1.1, pie-10.1.5)
- Libraries:
  - Lapack 3.3.1
  - HYPRE 2.7.0b

FSPAI is provided "as is", without warranty and support of any kind, express or
implied, including but not limited to the warranties of merchantability, fitness for a
particular purpose, title and non-infringement. In no event shall the copyright holders
or anyone distributing FSPAI be liable for any damages or other liability, whether in contract, tort or otherwise, arising from, out of or in connection with FSPAI or the use
or other dealings in FSPAI.

Some References