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, \(\mathbf{AX} = \mathbf{B}\), or \(\mathbf{A} ^T \mathbf{X} = \mathbf{B}\), or \(\mathbf{A} ^H \mathbf{X} = \mathbf{B}\), by the frontal method. The system may be real or complex (\(\mathbf{A} ^H\) denotes the conjugate transpose of \(\mathbf{A}\)). 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 \(\mathbf{A}\) must have a symmetric structure and must be in elemental form

\[\mathbf{A} = \sum _ {k=1} ^ {nelt} \mathbf{A} ^{[k]} ,\] where \(\mathbf{A} ^{[k]}\) 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 \(\mathbf{A}\) are associated with \(\mathbf{A} ^{[k]}\) and an array containing the nonzero entries. The right-hand sides \(\mathbf{B}\) may be supplied in elemental form (that is, \(\mathbf{B} = \sum _ {k=1} ^ {nelt} \mathbf{B} ^{[k]}\)) or in assembled form.

Precision: Double - Note: only double precision versions are provided, as we do not recommend this algorithm is used with 4-byte arithmetic.