Table of Contents

• Brief description
• Requested libraries
• Example of use
• Data-format
• Limitations
• Prerequesites
• Wrappers
• Make
• Full description
• License

Brief description

A generic API for using Sparse Direct Solvers, written in modern Fortran. It is designed to work with:

• MUMPS - MUltifrontal Massively Parallel sparse direct Solver ¹
• UMFPACK - Unsymmetric MultiFrontal method solver ²
• SuperLU - LU decomposition with partial pivoting and triangular system solves through forward and back substitution ³
• MA48 - Sparse unsymmetric system solver ⁴

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Requested libraries

• Generic
  
  • librefblas.a
  • liblapack.a
    
    
• MUMPS
  
  • libmetis.a
  • libmpiseq.a
  • libmumps_common.a
  • libdmumps.a
    
    
• UMFPACK
  
  • libamd.a
  • libcamd.a
  • libcolamd.a
  • libccolamd.a
  • libcholmod.a
  • libsuitesparseconfig.a
  • libumfpack.a
    
    
• SuperLU
  
  • libsuperlu.a
    
    
• MA48
  
  • libhsl_ma48.a

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Example of use

[[test_solvers]] proposes to test the solvers on two systems, a very small one and a "bigger" one. Some solvers have an "analyze" step during which symbolic factorization is performed. Hence if the sparsity of a new system does not change much, the symbolic factorisation is reused for the numerical factorization. To assess the time gained, after the first resolution other resolution are proposed with the same matrix pattern. After each resolution, the error is assessed remultipying the solution by the matrix and comparing it to the right-hand side.

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Data format

By default,

• UMFPACK and SuperLU are configured to read Compressed Column Harwell/Boeing formatted data,
  
  
• MUMPS reads elemental CC formatted data,
  
  
• MA48 reads sparse triplet formatted data.

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Limitations

The package MUSST is developped to handle some lubrication problems thanks to a multiscale approach. During the processe, sparse linear systems are solved either on concurrent threads or using all threads. In the first case, 'OpenMP' is not usefull because each thread is dedicated to the resolution of its own bunch of systems (Bottom Scale systems). In the second case, 'OpenMP' is desirable to speed up the resolution (Top Scale systems). For the moment, MUSST isn't designed for distributed shared memory architectures. Therefore the following choices are made:

• MUMPS is built with its sequential configuration (OpenMP, but not MPI). It is dedicated to TS systems.
  
  
• BLAS is built without OpenMP
  
  
• UMFPACK, SuperLU and MA48 are built without OpenMP. They are dedicated to BS systems.

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Prerequesites

The solver libraries must be downloaded and statically compiled together with their prerequisites:

• UMFPACK
  BLAS, LAPACK
  
  
• MUMPS
  BLAS, SCOTCH
  
  
• SuperLU
  BLAS
  
  
• MA48
  BLAS

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Wrappers

• UMFPACK
  A module [[mumfpack]] has been developped by Ladislav Hanyk. It has been checked with UMFPACK 5.6.2, but it also works fine here with UMFPACK 5.7.6.
  
  
• MUMPS
  A module [[mumps_wrapper]] is created with the content of dmumps_struc.h provided by MUMPS and it includes mpif.h, also provided by MUMPS. It is to be noticed that almost all global variables are deactivated in mpif.h.
  
  
• SuperLU
  A module [[sulu_wrapper]] is created from scratch because following SuperLU fortran examples (with the wrapper provided by SuperLU), we were not able to continuously solve systems with systematic memory release. As a consequence, the memory needed by MUSST increased untill the programs would stop.
  
  
• MA48
  In its double flavour, HSL_MA48 needs 3 files: common90.f90, ddeps90.f90 and hsl_ma48d.f90, renamed [[hsl_common90.f90]] and [[hsl_ddeps90.f90]] for the two first. In order to work with arrays independently from the solvers, the global solver type [[MAT_SOLV]] contains the system arrays --like eltptr, eltvar, a_elt, etc.-- pointed by a solver type, for instance [[ZD11_TYPE]]. Therefore, in version 3.3 of HSL_MA48, the attribute allocatable (in ZD11_TYPE) of row, col, ptr and val is changed to pointer.

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Make

General syntax:

make clean all "DEBUG=[yes,'']" "GPROF=[yes,'']"

Examples:

• first clean all, then make the 'debug' executable prg for profiling

make clean
make all "DEBUG=yes" "GPROF=yes"

• just build the modified sources, then make a productive executable

make all

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Full description

The aim of the present project is to provide generic subroutines for the direct full resolution of sparse linear systems:

• solver initialization

call solve_syst(mat=system_type, step='ini')

• system analyze

call solve_syst(mat=system_type, step='ana')

• system factorization

call solve_syst(mat=system_type, step='fac')

• system solution

call solve_syst(mat=system_type, step='sol')

• memory release

call solve_syst(mat=system_type, step='fre')

• solver finalization

call solve_syst(mat=system_type, step='end')

system_type is of complex type [[MAT_SOLV]] built to deal with MUMPS, UMFPACK, SuperLU and MA48 requirements.

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License

Footnotes

1. CeCILL-C license ↩

2. GNU GPL ↩

3. New BSD-3 ↩

4. HSL software is strictly intended for Personal academic use on the download page ↩