To solve one or more sets of sparse Hermitian or complex symmetric linear unassembled ﬁnite-element equations, , by the frontal method, optionally holding the matrix factor out-of-core in direct-access ﬁles. Numerical pivoting is not performed so for Hermitian matrices it is primarily designed for the positive-deﬁnite case. 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
ME62 stores the values of the entries in the factors and their indices separately. A principal feature of ME62 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.