h1. Numerical Problems
h2. What is the difference between numerical problems encountered during equation assembly and numerical problems encountered during equation solution?
{open-question}
h1. Lost Accuracy
h2. What does the lost accuracy warning message mean and how can I get rid of it?
The program performs most arithmetic with 15 digits of accuracy. When elements with significantly different stiffnesses are connected to a common joint, some digits of accuracy may be lost (for the element with smaller stiffness). Another example would be using rigid diaphragm assumption together with flexible elements. We recommend the following:
* *Less than 6 digits lost*: When we suspect that less than 6 digits of accuracy will be lost during solution we do not give any messages.
* *Between 6 to 11 digits lost* is reported as a warning: The results of the analysis may still be acceptable but we want the user to more carefully check the results especially the global sums of loads.
* *Above 11 digits lost* results in us terminating the program with an error message because we cannot trust the results. The model should be revised.
h2. What does the warning message "lost 6.4 digits of accuracy" mean?
SAP2000 equation solutions are performed in double precision arithmetic, which allows for 15 significant figures. If you have global or local instability (e.g., a node that is not restrained), the solution will suffer a loss of accuracy. The program issues a warning if the loss is estimated to be above 6 digits, and will cease processing if the detected loss is above 11 digits.
h2. How exactly does the program estimates the number of lost digits when accuracy is lost?
Lost digits are determined during the reduction of the stiffness matrix by comparing the order of magnitude of numbers that are being subtracted. The order of operations is based on the re-ordered equations, and so it is not always possible to predict the number that will be reported by the program or where it will be located. This algorithm does not check for the loss of accuracy that can occur during assembly, when two different stiffnesses are added together, rather it checks the accuracy of the solution of the assembled equations.
h2. What does the lost accuracy apply to? Displacements? Forces? Or both?
It applies to the terms of the stiffness matrix during the solution of the equation. Please see the above FAQ item for details on how the program determines the digits of lost accuracy. {{Verify}}
h2. I received a warning message for lost accuracy for body constraints. How are lost digits of accuracy calculated for body constraints?
[Body|Body constraint] and other rigid constraints create internal [master nodes|migration1d:master node] that become part of the system of equations. The constrained nodes are [slaves|migration1d:slave node] and are not part of the system of equations. So when the loss of accuracy occurs at the master node, it is reported to be for the constraint, rather than for any of the individual slave nodes.
Info
This page is devoted to frequently asked questions (FAQ) related to numerical problems.
On this page:
Table of Contents
What does the Lost Accuracy warning message indicate, and how is it resolved?
Answer: For response, please see the Lost accuracy article.
What does the Lost 6.4 Digits of Accuracy warning message indicate?
Answer: Equation solutions are performed in double-precision arithmetic to provide for 15 significant figures. If global or local instability occurs, for example when a restraint is not assigned to a support, lost accuracy will occur. If this loss is estimated to be in excess of six digits, a warning message will be issued, and when in excess of 11 digits, numerical formulation will cease to process.
How is the number of lost digits of accuracy estimated?
Answer: The number of lost digits is determined during the reduction of the stiffness matrix through comparison of the order of magnitude of the values being subtracted. The operation sequence is based on the reorder equations, therefore it is not always possible to compute the exact number of digits lost, and the location of the occurrence. As a result, quantity and location may be estimated. Note that accuracy is checked during solution of the assembled equations, and not during assembly, when stiffnesses are added together.
To what does lost accuracy apply?
Answer: Lost accuracy applies to the stiffness matrix and its values during numerical solution. Since stiffness governs the relationship between force and displacement, lost accuracy will affect both of these response measures.
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I received a body-constraint lost-accuracy warning message. How is this calculated?
Answer:Body and other rigid constraints create an internal master node which governs the nodes assigned to the constraint. These master nodes become part of the system of equations while the constrained nodes do not. When lost accuracy occurs within the constraint, it is reported for the master node, and not the individual components.
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What causes the numerical problem Diagonal < 0, and how is it resolved?
OPEN QUESTION
Possible causes:
For linear analysis, Diagonal < 0 could result from an , in which constrained points are not exactly on the edge.
See 9/2/2010 email from fs, ID 3705068
For analysis, when effect is considered, negative terms may occur on the diagonal of the stiffness matrix at the onset of .
See Incident 27490 - example of Diagonal < 0 numerical problem.
What is the difference between equation-assembly and equation-solution numerical problems?