A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications

Reviewer: Ian Gladwell

The authors develop a new frontal code, MA62 in the Harwell subroutine library, for solving sparse, positive definite, linear symmetric systems. The matrices must arise from a finite element analysis, because a crucial part of the frontal approach is to exploit the assembly of the finite element equations in determining the current “front.” The MA62 code has three phases. First, a prepass and symbolic analysis phase determines when each element will be fully assembled and hence may be eliminated. This phase also determines the storage requirements of the solver; there is no pivoting, so the storage required may be determined a priori. The second phase factors the assembled matrix and solves for right-hand sides that also arise from assembled elements. The third phase solves for further right-hand sides, which need not arise from element assembly. The code permits the use of secondary storage via direct access files; uses level 3 Basic Linear Algebra Subroutines (BLAS) where possible; permits user specification of internal block sizes; and, optionally, exploits zeros in the assembled front. This detailed paper contains many comparisons demonstrating the effectiveness of its various options, and makes a strong case for the use of an element ordering preprocessor (also available from the Harwell library). There are also (mainly favorable) comparisons with MA42, a general-purpose frontal solver in the Harwell library, and with other software being developed for this problem .