Software Option for Standard
and Plus versions
Fast Solvers
Additional solvers, provided as a single product option, are available for use with any
currently supported LUSAS software product.
Fast
Multifrontal Direct Solver
The
Fast Multifrontal Direct Solver is an implementation of the
multifrontal method of Gaussian Elimination, and uses the modern
sparse matrix technology of assembling a global stiffness matrix where
only the nonzero entries are stored. The solver
can be used for almost all types of analysis, and has extensive
pivoting options to ensure numerical stability, especially for
symmetric problems. It is
particularly fast at solving large 3D solid models.
The solver employs powerful
reordering algorithms that minimise the amount of extra nonzero
entries that are created during the elimination process (known as fillin
entries). As a result, the disk space requirements are typically 75%
less than that of the standard frontal direct solver. An advanced
outofmemory facility means that problems which exceed the memory
capabilities of the machine can still be solved.
A data check facility is provided
and a resolution facility, as with the standard Frontal Direct solver,
enables you to rerun linear analyses with different loadcases without
having to eliminate the stiffness matrix. Various checks are made to
see if the solution vector has been corrupted by roundoff error, and
warnings are issued accordingly. An estimate of the condition number
of the matrix is also computed, so that the relative error in the
solution (with respect to machine precision) can be predicted. The
solver also recognises negative and nearzero pivots, and will give
diagnostic warning messages in each case relating to a particular node
and variable in the model.
Fast Multifrontal Block
Lanczos EigenSolver
The
Fast Multifrontal Block Lanczos Eigensolver is based on the Shift and
Inverse Block Lanczos algorithm, and solves natural frequency,
vibration and buckling problems with real, symmetric matrices. It is
very fast, extremely robust, and ensures that convergence is almost
always achieved.
You can specify the lowest, highest
or a range of eigenvalues to be returned, along with the normalised
eigenvectors and error norms which are currently given with the
standard Frontal Eigensolvers. The Fast Multifrontal Block Lanczos
Eigensolver is based on the same underlying technology as the new Fast
Multifrontal Direct Solver and has the same pivoting options, error
diagnostics and outofmemory facilities. An internal Sturm sequence
check is performed to verify that the eigenvalues returned are those
requested, and you can specify combinations of eigenvalues to be
returned in the same analysis, as for example, the highest three
eigenvalues can be specified, followed by the lowest ten, and all
those in the range 0 to 50.
Complex
Eigensolver
The complex
eigensolver is nonsymmetric eigen solver based on an implicitly
restarted Arnoldi method. It provides solutions to damped
natural frequency problems for both solid and fluid mechanics. It can
solve large scale problems with real, nonsymmetric input matrices (in
particular, those involving nonproportional damping), and gives
solutions that consist of complex numbers where appropriate.
Fast Parallel Direct
Solver and Fast Parallel Iterative Solver
These solve large sparse
symmetric and nonsymmetric equations on shared memory
multiprocessors.
"Upgrading
to the LUSAS Fast Solvers option for our work gave us an
estimated 5 to 10 times speedup of our solution times"
Mike Gower, Research
Scientist, National Physical Laboratory, UK

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