r3.03.05 Elimination of dualized boundary conditions

Summary:

The consideration of boundary conditions in c*ode_aster* can be achieved either by a direct elimination technique in simple cases (AFFE_CHAR_CINE), or by using a dualization technique (AFFE_CHAR_MECA), and the introduction of Lagrange multipliers, for the most general cases.

However, this approach has two drawbacks. On the one hand, the addition of Lagrange multipliers increases the number of degrees of freedom of the global problem, and therefore the size of the system to be solved. This point can become a disadvantage as the number of boundary conditions increases (numerous interfaces, kinematic links, rigid motion impositions, etc.). On the other hand, the particular dualization technique leads to the loss of the positive semi-definite character of the stiffness matrix. This change in nature can lead to robustness defects, or even to the failure of resolution in the case of iterative solvers.

This document presents a method for eliminating Lagrange multipliers a posteriori in order to take account of affine boundary conditions. This approach does not concern the Lagrange multipliers linked to contact modeling.

The elimination of boundary conditions is achieved either by using the ELIM_LAGR keyword in SOLVEUR [U4.50.01], or directly with the ELIM_LAGR [U4.55.03] operator which builds a new concept matr_asse_elim.

• 1. Notations
• 2. Introduction
• 3. Principle of resolution by elimination
  • 3.1. Definition of the problem to be solved
  • 3.2. Search for the particular solution
  • 3.3. Finding the general solution
• 4. Clean modes and disposal
• 5. Bibliography