Parallel processing for Ritz vector analysis
Prior to beginning Ritz analysis, the machine running ETABS uses multiple cores to factor the stiffness matrix. During Ritz analysis, four main operations include:
- Solving for new vectors
- Cleaning new vectors with respect to previous vectors
- Orthogonalizing the final Ritz vector set
- Post-processing and saving the vectors
Only the first step uses multi-cores. This step dominates for problems where the model is large and a fair number of vectors are requested. Steps (2) and (3) are not parallelized, and they dominate as the number of vectors is increased. Step (4) is linear in time with the number of vectors. When large number is Ritz vectors is being requested, steps (2) and (3) will dominate, and will increase exponentially with more vectors.
However, the usual intention for using Ritz or eigen vectors is that they reduce the number of degrees of freedom in the system, so that the essential behavior can be captured more efficiently. If you need much more than about 20 to 25% of the DOF as Ritz vectors, you may want to consider direct-integration.
Why is the cumulative modal mass participation ratio for a given number of Ritz vectors affected by the total number of Ritz vectors requested?
Extended Question: When 1000 Ritz modes are requested, the cumulative modal mass participating ratios for Rx for 250 modes is almost 100%. However, when only 500 modes are requested, the cumulative modal mass participating ratio for Rx reaches only about 70% for all 500 modes. Is there any explanation for this?
Answer: Unlike Eigen vectors, Ritz vectors do not always produce the same modes. For example, if you get 200 and 500 eigens, the first 200 of both will be the same. But if you get 200 and 500 Ritz vectors, none may be the same, although the lower modes will tend to converge to be the same as you increase the number of modes.