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31st March 2023

MA46: Sparse unsymmetric finite-element system: multifrontal

To solve one or more set of sparse unsymmetric linear equations \(\bf AX = \bf B\) from finite-element applications, using a multifrontal elimination scheme. The matrix \(\bf A\) must be input by elements and be of the form \[\mathbf{ A} = \sum_ {k=1} ^ m \mathbf {A} ^{(k)}\] where \(\mathbf {A} ^{(k)}\) is nonzero only in those rows and columns that correspond to variables of the nodes of the \(k\)-th element. Optionally, the user may pass an additional matrix \(\mathbf {A} _d\) of coefficients for the diagonal. \(\mathbf {A}\) is then of the form \[\mathbf {A} = \sum_ {k=1} ^ m \mathbf {A} ^{(k)} + \mathbf {A} _d\] The right-hand side \(\bf B\) should be assembled through the summation \[\mathbf {B} = \sum_ {k=1} ^ m \mathbf {B} ^{(k)},\] before calling the solution routine.