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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

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.