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9th April 2013 User documentation
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MA42: Sparse unsymmetric system: outofcore frontal method
To solve 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 directaccess files for the matrix factors. Use is made of high level BLAS kernels. The code has low incore memory requirements. The matrix \(\mathbf{A}\) may be input by the user in either of the following ways:
(i) by elements in a finiteelement calculation,
(ii) by equations (matrix rows).
In both cases, the coefficient matrix and righthand 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. \(\mathbf{A} ^{(k)}\) is nonzero only in those rows and columns which correspond to variables in the \(k\)th element. \(\mathbf{b} ^{(k)}\) 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 \(k\).