Differences

This shows you the differences between two versions of the page.

--- wiki:sns:sns2014:resolution_and_convergence [2017/07/14 09:11] – claire
+++ wiki:sns:sns2014:resolution_and_convergence [2017/07/17 10:03] (current) – claire
@@ Line 1: / Line 1: @@
+~~NOTOC~~
 ====== Resolution and Convergence ======
@@ Line 8: / Line 9: @@
     * You may run out of memory and/or will have to wait for a long time to get your solution, which will still only be a numerical approximation of an idealized model of physical reality.
     * To see if the solution is converging, you need to compare the solutions at several different resolutions.
+**To learn more on how to pick the proper resolution for analysis, read this [[wiki:sns:sns2014:select_resolution|document]].**
 ===== Convergence =====
@@ Line 15: / Line 18: @@
 To establish that the solution converged, solve the same problem a number of times, gradually increasing the resolution, until displacement values stay approximately in the same range. If displacement does not converge, there is no guarantee that the numerical solution is accurate.
-If computed displacement values did converge, one can also study convergence of stresses. But it is important to remember that the linear theory of elasticity (used by every structural analysis software, including the present version of Scan&Solve™) predicts infinite stresses near "wedges," re-entrant corners, interfaces between different materials, and and other //singularities//. In physical reality, this cannot happen, because the material simply deforms more "plastically" (as opposed to "elastically"). This means that at some points in a model, stresses may never converge -- they will just get bigger and bigger as you increase the resolution. The more complex your model is, the more likely you will have some singularities like that. It does make sense to study convergence of stress values at particular locations in the model that are away from singularities.
+If computed displacement values did converge, one can also study convergence of stresses. But it is important to remember that the linear theory of elasticity (used by every structural analysis software, including the present version of Scan&Solve™) predicts infinite stresses near "wedges," re-entrant corners, interfaces between different materials, and other //singularities//. In physical reality, this cannot happen, because the material simply deforms more "plastically" (as opposed to "elastically"). This means that at some points in a model, stresses may never converge -- they will just get bigger and bigger as you increase the resolution. The more complex your model is, the more likely you will have some singularities like that. It does make sense to study convergence of stress values at particular locations in the model that are away from singularities.
 The solution of the problem may not always converge, even for displacement. There are several reasons for this.
@@ Line 22: / Line 25: @@
 Are converged solutions always correct? No. Every numerical procedure has its limitations, and Scan&Solve™ is no exception. The correctness of computed results depends on specific elements used in the solution procedure and individual steps in the procedure process, including function and solid sampling, surface and volume integration, and the solution of linear system of equations. To validate the solution procedure, it is highly advised to test it against a variety of similar and different problems, as well as on problems with known solutions.
+**The convergence checking process can be automated in SnSScript. Read [[wiki:sns:sns2014:check_convergence_of_a_scenario|this document]] to learn how to easily create a convergence plot with SnSScript.**