The frontal method was first conceived (Irons, 1970) for symmetric positive-definite finite-element problems, but it has since been extended to handle unsymmetric matrices and matrices that do not originate from finite-element problems. It has also been extended to the multifrontal method that is better able to preserve the sparsity and is used now, for example, by Nastran.

The first part of this talk will explain the methods, assuming only that the audience is familiar with Gaussian elimination (all these methods are variants of Gaussian elimination).

The second part of the talk will review the frontal and multifrontal work of the Numerical Analysis Group at the Rutherford Appleton Laboratory. This has led to many Fortran codes that are available in HSL (formerly Harwell Subroutine Library) and to a Fortran/MPI code that was one of the deliverables of the ESPRIT IV project PARASOL.