| Author | Message | |||
     Steven E. Williamson (sew) Member Username: sew Post Number: 4 Registered: 02-2008 |
I discovered what I think may be a "typo" in the current version of the "FlexPDE 5.0 Reference Manual". On p. 32, the following lines appear: "Integrals of this type may be further qualified by selecting the region in which the evaluation is to be made: SURF_INTEGRAL( integrand, named_boundary, named_layer, named_region ) named_region must be one of the regions bounded by the selected surface." If one actually does this, the error: "The Selector named_region is Undefined" is produced. But by inverting the layer and region specifications, the surface integral is evaluated properly. So it seems like the correct form for a fully qualified surface integral in 3D is: SURF_INTEGRAL( integrand, named_boundary, named_region, named_layer ) I have attached a simple .pde script to illustrate this. The geometry is an inverted U-shaped object. The equation is the static heat equation. Temperatures are specified on the bottoms of the legs of the U. Three regions are defined (one for each leg and one for the top bar that spans between the two legs). Integrals of heat flux are done on intermediate surfaces. To specify where the integral is to be done, a combination of surface, layer, and region are needed. Specifying only the surface and region works, i.e.: SURF_INTEGRAL( integrand, named_boundary, named_region ) but the side of the surface to be integrated (and therefore the sign of the integral) is not then well defined so some default is used.
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1071 Registered: 06-2003 |
The text of page 32 that you quote refers to "sidewall" integrals, and the indicated "named_boundary" means a region-bounding path. Your example problem has no named sidewall boundaries, so the forms described on page 32 cannot be invoked. Did you send the wrong example? | |||
| Steven E. Williamson (sew) Member Username: sew Post Number: 6 Registered: 02-2008 |
No, I sent the right file ... BUT now I think I understand what's going on. I read through the section on 3D surface integrals too fast and got confused by the fact that for integrals over extrusion surfaces, the syntax is: SURF_INTEGRAL(integrand,surface,region,layer) BUT for side-walls, it is: SURF_INTEGRAL(integrand,boundary,layer,region) I didn't notice that the region/layer specifications reverse in these two cases. So there is no "typo". (Out of curiosity, though, is there a reason for this reversal?) By the way, thanks for your patience with my questions. | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1075 Registered: 06-2003 |
The reversal of order was to support a form without the last argument. For an extrusion surface, the resonable form selects a region, while on a sidewall, the resonable form selects a layer. |
