d9.03.02 Implementing the multifrontal method MULT_FRONT

Summary:

In this note, we present the computer description of the native version in Code_Aster, of the multi-frontal linear solver, commonly called MULT_FRONT.

This version, developed at EDF R&D, is stable, with an almost complete scope.

This note complements the Code_Aster reference documentation: « Linear solver using the multi-frontend method » [R6.02.02].

We recall the main concepts used by the method: renumbering, elimination tree, supernodes. The computer structures created by the algorithm are described. The main computer difficulties and particularities are reported. We are considering the various possible developments.

A report published separately is dedicated to an overview and the prospects for application maintenance: [RB12] « Native multi-frontend method in Code_Aster: state of play and perspectives », CR-I23-2012-001.

Table of Contents

• 1. Introduction
  • 1.1. General principles.
  • 1.2. Programming the method.
• 2. Renumbering and symbolic factorization: MLTPRE
  • 2.1. PREML0
  • 2.2. PREMLA
  • 2.3. PREML1
  • 2.4. PREMLC
  • 2.5. PREMLD
  • 2.6. PREML2
  • 2.7. MLTPRE call tree
• 3. Numerical factorization MULFR8
  • 3.1. MLTASA
  • 3.2. MLTFC1
• 4. System upgrade: RLTFR8
  • 4.1. MLTDRA
  • 4.2. RLBFR8
• 5. Non-symmetric version
• 6. Complex version
  • 6.1. Symmetric complex factorization
  • 6.2. Non-symmetric complex factorization
  • 6.3. Complex descent and ascent
• 7. Parallelization
• 8. Various remarks
• 9. Conclusions, possible developments.
  • 9.1. Scope of execution
  • 9.2. Performance
• 10. References.