(3M) Calculator User Manual

Description
The gord prog ram is the block sparse matrix graph o rderer. It uses an or-
dering strategy to compute block orderings of sparse matrices represented a s
source graphs, whose vertex weights indicate the number of DOFs per node (if
this number is non homogeneous) and whose edges are unweighted, in order
to minimize fill-in and operation count.
Since its main purpose is to provide order ings that exhibit high concurrency
for parallel block factorization, it comprises a nested dissection method [17],
but classical [39] and state-of-the-art [1, 47] minimum degree algorithms are
implemented as well. Ordering methods are used to define ordering strateg ie s
by means of selection, grouping, and condition operators.
For the nested dissection method, vertex separation methods comprise algo-
rithms that directly compute vertex separators, as well as methods that build
vertex separators from edge separators , i.e. graph bipartitions (all of the graph
bipartitioning methods available in the s tatic mapper gmap can be used in this
latter case).
The -o optio n allows the user to define the ordering strategy. The -c option
allows the user to set preferences on the behavior of the ordering strategy
which is used by default.
When the graphs to order are very large, the same results can be obtained by
using the dgord parallel progra m of the PT-Scotch distribution, which can
read centralized graph files too.
Options
Since the program is devoted to experimental studies, it has many optional
parameters, used to test various execution modes . Values set by default will
give best results in most cases.
-cflags
Tune the default ordering strategy according to the given preference flags.
Some of these flags are antagonistic, while others can be combined. See
Section 7.3.1 for more information. The resulting strategy string can be
displayed by means of the -vs option.
b Enforce load balance as much as possible.
q Privilege quality over speed. This is the default behavior.
s Privilege sp e ed over quality.
t Use only safe methods in the strategy.
-h Display the program synopsis.
-moutput
mapping file
Write to output
mapping file the mapping of graph vertices to column
blocks. All of the separator s and leaves produced by the nested dissection
method are co ns idered as distinct column blocks, which may be in turn
split by the ordering methods that are applied to them. Distinct integer
numbers are associated with each of the column blocks, such that the
number of a block is always greater than the ones of its predecessors in
the elimination proce ss, that is, its descendants in the elimination tree.
The structure of mapping files is given in section 5.5.
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