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h1h2. Parallel processing for Ritz -vector analysis

Prior to beginning Ritz analysis, the machine running [ETABS|etabs:Home] uses multiple cores to factor the stiffness matrix. During Ritz analysis, four main operations include:

# Solving for new vectors
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# Cleaning new vectors with respect to previous vectors
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# Orthogonalizing the final Ritz vector set
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# Post-processing and saving the vectors

OnlyMultiple thecores firstare stepused uses multi-cores. This steponly for (1), which dominates for problems wherewhen the model is large and a fair number of vectors are requested. Steps (2) and (3) are not parallelized, and theydominate dominatewith asan theincreasing number of vectors is increased, growing exponentially with vector quantity. Step (4) is linear in time with the number of vectors.
When
largeEssential numberbehavior is Ritz vectors is being requested, steps (2) and (3) will dominate, and will increase exponentially with more vectors.

However, the usual intention for captured more efficiently when using Ritz or eigenEigen vectors is thatbecause they reduce the number of degrees of freedom (DOF) inwithin the system, so that the essential behavior can be captured more efficiently. If you need much. When more than about 20 to -25% of the DOF are needed as Ritz vectors, youdirect mayintegration wantshould to consider direct-integrationbe considered.


h2. Why is does the total number of Ritz vectors requested affect 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 participatingparticipation ratiosratio for Rx, forwith 250 modes, is almost 100%. However, when only 500 modes are requested, the cumulative modal mass participatingparticipation ratio for Rx reaches only about 70% for all 500 modes. Is there anyan explanation for this?

*Answer:* Unlike Eigen vectors, Ritz vectors do not always produce the same modes. For example, ifwith yousets getof 200 and 500 Eigen eigensvectors, the first 200 of botheach set will be the same. ButHowever, ifwith yousets getof 200 and 500 Ritz vectors, none may be the same, although thethough lower modes will tend to converge to be the same as you increase the number of modes increases.


{related-incident:no=20000|comment=See action request "cumulative mass participating ratios for Ritz Vector modal analysis" from 3/29/2010.}