## Version 2.0.0

9th April 2013

Recent Changes

• Single
• Double
• Single Complex
• Double Complex

### 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 $n×n$ 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.