To solve one or more sets of sparse symmetric linear unassembled ﬁnite-element equations, , by the frontal method, optionally holding the matrix factor out-of-core in direct-access ﬁles. The package is primarily designed for positive-deﬁnite matrices since numerical pivoting is not performed. Use is made of high-level BLAS kernels. The coeﬃcient matrix must of the form
with nonzero only in those rows and columns that correspond to variables in the -th element.
The frontal method is a variant of Gaussian elimination and involves the factorization
where is a permutation matrix, is a diagonal matrix, and is a unit lower triangular matrix. The solution process is completed by performing the forward elimination
followed by the back substitution
MA62 stores the reals of the factors and their indices separately. A principal feature of MA62 is that, by holding the factors out-of-core, large problems can be solved using a predetermined and relatively small amount of in-core memory. At an intermediate stage of the solution, say, the ‘front’ contains those variables associated with one or more of , , which are also present in one or more of , . For eﬃciency, the user should order the so that the number of variables in the front (the ‘front size’) is small. For example, a very rectangular grid should be ordered pagewise parallel to the short side of the rectangle. The elements may be preordered using the HSL routine MC63.