# How to discretize parametric curves for FEM analysis

I would like to know if there is anything available in order to discretize a 3D curve given by parametric equations in order to apply FEM analysis, e.g. to solve the wave equation on a thin wire with the shape of the given curve.

## 2 Answers

No, you have to discretize the wire fully; alternatively you could find a mapping of your wire to 1D and go from there.

It can be done easy in MMA 11, just define the Region-wire by built-in functions

ir = ParametricRegion[{Cos@t, (Sin@t)^2, 10/(t + 0.1)^0.5}, {{t, 0, 6 π}}]
DiscretizeRegion[ir]


• When I run it to MA 11 the following error message appears : "DiscretizeRegion did not find any sample points in the region ParametricRegion[<<2>>] with bounds {{-1.,1.},{0.,1.},{2.29721,31.6228}}. If this is not correct, different bounds may help" – DK13 Jul 25 '17 at 9:50
• Also the depicted curve is 2D while in the parametricregion command you used a 3D representation – DK13 Jul 25 '17 at 10:39
• In my case (MMA 11.1), it is working without error-messages. This figure is namely 3D figure which can be rotated as you wish. And the region is in common the 3D-region. – Rom38 Jul 26 '17 at 4:14
• Ok the 11.1 version is capable for this discretization, but the NDSolve and NDSolveValue commands cannot solve a PDE on this curve. It returns "The current version of NDSolve cannot solve equations over boundaries or surfaces. Please specify a region where the embedding dimension is the same as the dimension."... Any idea? – DK13 Jul 26 '17 at 11:13
• Guys, what was an initial question? I guess, "How to discretize parametric curves for FEM analysis" means that answer have to be about discretization, or not? There is not a problem with discretization, it is easy. The main problem of topic starter (as it is evident now) is about how to use the obtained mesh. Unfortunately, Wolfram have failed the realization of the FEM.. – Rom38 Jul 27 '17 at 3:46