### HSL_MA42_ELEMENT Unsymmetric ﬁnite-element system: out-of-core frontal
method (real and complex)

HSL_MA42_ELEMENT solves one or more sets of sparse linear unsymmetric unassembled ﬁnite-element
equations, $AX=B$,
or ${A}^{T}X=B$, or
${A}^{H}X=B$,
by the frontal method. The system may be real or complex
(${A}^{H}$ denotes the conjugate
transpose of $A$).
There are options for automatically ordering the elements, for supplying the elements
using a reverse communication interface, for holding the matrix factors in
direct-access ﬁles, and for preserving a partial factorization.

The $n\times n$
coeﬃcient matrix $A$
must have a symmetric structure and must be in elemental form

$$A=\sum _{k=1}^{nelt}{A}^{\left[k\right]},$$

where ${A}^{\left[k\right]}$
is nonzero only in those rows and columns that correspond to variables in the
$k$-th ﬁnite element.
The elements must be square elements, with the row indices equal to the column indices.
For each $k$,
the user must supply a list specifying which rows/columns of
$A$ are associated
with ${A}^{\left[k\right]}$
and an array containing the nonzero entries. The right-hand sides
$B$ may be supplied in
elemental form (that is, $B={\sum}_{k=1}^{nelt}{B}^{\left[k\right]}$)
or in assembled form.

Precision: At least 8-byte arithmetic is recommended.