r6.02.02 Linear solver using the multifrontal method MULT_FRONT

Summary:

The multifrontal method MULT_FRONT is a direct method particularly suited to the resolution of linear systems whose matrix is sparse. This method includes a preliminary renumbering phase intended to minimize the filling of the matrix during factorization.

This phase also makes it possible to group variables into « super-variables » or « super-nodes ». Factorization, on the other hand, is carried out in the form of a sequence of elimination of supernodes, in full matrices. These full matrices allow the use of optimized routines like BLAS, which obtain the best performances on vector or scalar machines.

With the factored matrix, each system resolution will only require an inexpensive « descent/ascent ».

Table of Contents

• 1. Description of the method
  • 1.1. Method LDLT for full matrices
  • 1.2. Hollow matrix and filling
  • 1.3. Multifrontal method
  • 1.4. Descent - Lift
• 2. Implementation and use in Code_Aster
• 3. Bibliography
• 4. Description of document versions