Overview

STRUMPACK - STRUctured Matrix PACKage - is a software library providing linear algebra routines and linear system solvers for sparse and for dense rank-structured linear systems. Many large dense matrices are rank structured, meaning they exhibit some kind of low-rank property, for instance in hierarchically defined sub-blocks. In sparse direct solvers based on LU factorization, the LU factors can often also be approximated well using rank-structured matrix compression, leading to robust preconditioners. The sparse solver in STRUMPACK can also be used as an exact direct solver, in which case it functions similarly as for instance SuperLU or superlu_dist. The STRUMPACK sparse direct solver delivers good performance and distributed memory scalability and provides excellent CUDA support.

Currently, STRUMPACK has support for the Hierarchically Semi-Separable (HSS), Block Low Rank (BLR), Hierachically Off-Diagonal Low Rank (HODLR), Butterfly and Hierarchically Off-Diagonal Butterfly (HODBF) rank-structured matrix formats. Such matrices appear in many applications, e.g., the Boundary Element Method for discretization of integral equations, structured matrices like Toeplitz and Cauchy, kernel and covariance matrices etc. In the LU factorization of sparse linear systems arising from the discretization of partial differential equations, the fill-in in the triangular factors often has low-rank structure. Hence, the sparse linear solve algorithms in STRUMPACK exploit the different dense rank-structured matrix formats to compress the fill-in. This leads to purely algebraic, fast and scalable (both with problem size and compute cores) approximate direct solvers or preconditioners. These preconditioners are mostly aimed at large sparse linear systems which result from the discretization of a partial differential equation, but are not limited to any particular type of problem. STRUMPACK also provides preconditioned GMRES and BiCGStab iterative solvers.

Apart from rank-structured compression, the STRUMPACK sparse solver also support compression of the factors using the ZFP library, a general purpose compression algorithm tuned for floating point data. This can be used with a specified precision, or with lossless compression.

The HODLR and Butterfly functionality in STRUMPACK is implemented through interfaces to the ButterflyPACK package:

• https://github.com/liuyangzhuan/ButterflyPACK

Check the STRUMPACK github page for the latest development version of the code, and the website for more information:

• https://github.com/pghysels/STRUMPACK
• http://portal.nersc.gov/project/sparse/strumpack/

For comments, feature requests or bug reports, open an issue on github:

• https://github.com/pghysels/STRUMPACK/issues

Table of Contents

• Installation and Requirements
• GPU Support
• Sparse Direct Solver
  • Algorithm Overview
  • Example Usage
• Precontioning
  • BLR Preconditioning
  • HODLR & HODBF Preconditioning
  • HSS Preconditioning
  • Lossy/Lossless Compression Preconditioning
• Dense Solvers
  • Block Low Rank (BLR) Approximation
  • Hierarchically Off-Diagonal Low-Rank (HODLR) and Butterfly Approximation
  • Hierarchically Semi-Separable (HSS) Matrix Approximation
• Examples
• C and Fortran Interfaces
• FAQ
• Contact Authors
• Acknowledgements
• Copyright Notice and License Agreement
• References

Current developers - Lawrence Berkeley National Laboratory

• Pieter Ghysels - pghys.nosp@m.els@.nosp@m.lbl.g.nosp@m.ov
• Xiaoye S. Li - xsli@.nosp@m.lbl..nosp@m.gov
• Yang Liu - liuya.nosp@m.ngzh.nosp@m.uan@l.nosp@m.bl.g.nosp@m.ov
• Lisa Claus - LClau.nosp@m.s@lb.nosp@m.l.gov

The STRUMPACK project started at the Lawrence Berkeley National Laboratory in 2014 and is supported by the FASTMath SciDAC Institute funded by the Department of Energy and by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.