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HSL_MA42: Sparse unsymmetric system: out-of-core frontal method

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The module `HSL_MA42`

solves one or more sets of sparse linear equations, \(\mathbf{Ax} = \mathbf{b}\) or \(\mathbf{A} ^T \mathbf{x} = \mathbf{b}\), by the frontal method, optionally using direct-access files for the matrix factors. Use is made of high level BLAS kernels. The code has low in-core memory requirements. The matrix \(\mathbf{A}\) may be input by the user in either of the following ways:

(i) by elements in a finite-element calculation,

(ii) by equations (matrix rows).

In both cases, the coefficient matrix and right-hand side(s) are of the form

\[\mathbf{A} = \sum _ {k=1} ^ m \mathbf{A} ^{(k)} ,\qquad
\mathbf{b} = \sum _ {k=1} ^ m \mathbf{b} ^{(k)}.\]

In case (i), the summation is over finite elements. The matrix \(\mathbf{A}
^{(k)}\) is nonzero only in those rows and columns which correspond to variables in the \(k\)-th element. The vector \(\mathbf{b} ^{(k)}\) is nonzero only in those rows which correspond to variables in element \(k\).

In case (ii), the summation is over equations and \(\mathbf{A} ^{(k)}\) and \(\mathbf{b} ^{(k)}\) are nonzero only in row \(k\).