### MA46 Sparse unsymmetric ﬁnite-element system: multifrontal

To solve one or more set of sparse unsymmetric linear equations
$AX=B$ from
ﬁnite-element applications, using a multifrontal elimination scheme. The matrix
$A$ must
be input by elements and be of the form

$$A=\sum _{k=1}^{m}{A}^{\left(k\right)}$$
where ${A}^{\left(k\right)}$ is
nonzero only in those rows and columns that correspond to variables of the nodes of the
$k$-th
element. Optionally, the user may pass an additional matrix
${A}_{d}$ of coeﬃcients for
the diagonal. $A$
is then of the form

$$A=\sum _{k=1}^{m}{A}^{\left(k\right)}+{A}_{d}$$
The right-hand side $B$
should be assembled through the summation

$$B=\sum _{k=1}^{m}{B}^{\left(k\right)},$$
before calling the solution routine.