HSL_MA78
Out-of-core Sparse Unsymmetric Element Solver
HSL_MA78 is designed to efficiently solve unsymmetric sparse linear systems that arise from element problems and are so large they cannot be solved in memory. By holding the data and work arrays in files on disk, the memory requirements are limited, enabling HSL_MA78 to solve much larger problems than is possible with a conventional sparse direct solver.
Note: For symmetric systems, HSL_MA77 should be used.
Functionality
- multifrontal algorithm to solve sparse unsymmetric systems Ax=b arising from element problems using the factorization A = PLDUQ.
- Option to solve transpose systems ATx=b.
- A input by element-by-element so that holding A in memory is avoided.
- Flexible out-of-core working for large matrices.
- Out-of-core scaling.
- Range of pivoting options.
- Preserve factors on disk between runs.
- Can be used to solve the related systems PLx = b and DUQx = b.
Performance
- Solves much larger problems than conventional sparse direct solvers.
- Factorization time generally significantly less than for a uni-frontal solver.
- The overhead of working out-of-core is minimised through the use of our specially-designed virtual memory system (HSL_OF01).
Numerical results are presented in [1] and [2].
Availability
We offer both in-house usage and incorporation licences for HSL_MA78. It is freely available for academic use. Please see our website, or email us at hsl@stfc.ac.uk for further details. Development was funded by EPSRC grant EP/E053351/1.[1] J. K. Reid and J. A. Scott, An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems, Technical Report RAL-TR-2007-014.
[2] J. A. Scott, Scaling and pivoting in an out-of-core sparse direct solver, Technical Report RAL-TR-2008-016.