r5.06.01 Model reduction in linear and non-linear dynamics: RITZ method

Summary:

This document presents the principle of model reduction by projection on a reduced base (Ritz method).

The most commonly used base is the modal base.

Truncation problems due to the use of a reduced base are mentioned. Truncation corrections are proposed.

The description and the properties of the algorithms for solving the system of second-order differential equations obtained in transient analysis are presented in the document [R5.06.04].

• 1. Introduction
• 2. Linear Ritz reduction methods
  • 2.1. General description
  • 2.2. Projection on a reduced base
  • 2.3. Projection on a modal basis
  • 2.4. Modal truncation error
  • 2.5. Modal truncation corrections
• 3. Extending Ritz reduction methods to nonlinear
  • 3.1. General problem
  • 3.2. Indication of projection error
• 4. Use in Code_Aster
• 5. Bibliography
• 6. Description of document versions