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

The module HSL_MA42 solves one or more sets of sparse linear equations, $Ax=b$ or $A^{T}x=b$, 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 $A$ 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

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

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