Jens
Reputation
65,725
1422/1000 score
 Jan 27 comment Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ You're welcome. The question may be closed, but I think you may be interested in this link for the visualization of the nodal lines. Perhaps you can re-direct your question if the visualization aspect is still something you want to see improved. Jan 27 comment Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ Yes, that's correct. Jan 27 comment Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ FEM doesn't use assumptions about separability. But this is what the textbook labeling scheme of the eigenfunction is based on. So the only criterion by which FEM is able to sort the solutions is their eigenvalue. Node numbers based on separability provide a different sorting scheme but not in brute-force approaches such as this. I use "energy" above, but you can omit that term. It's an interpretation only. Jan 27 comment Numerically Solving Helmholtz over the Rectangle - Why does this code only give eigenfunctions of the form $u_{m1}$ The eigenfunctions are sorted by their energy eigenvalue, and $u_{1,2}$ is higher than you probably expected. It is found as evIF[[4]]. So there seems to be no problem. Other eigenfunctions may have degeneracies that will lead to superpositions with nodal lines that aren't straight lines. So I think there is no problem with Mathematica's solutions. Jan 27 revised Inset in ArrayPlot edited tags Jan 27 comment NDEigensystem producing imaginary eigenfrequencies for the vibrations of a cantilever The imaginary eigenvalues turn real if I set Dirichlet conditions on the entire boundary. So I guess it's got something to do with the Neumann conditions. Looks like a bug, but needs further investigation... I was able to suppress the imaginary parts in the first approach (with your Dirichlet condition) by increasing "MaxCellMeasure" -> (1/800). But they don't go away completely... Jan 27 reviewed Approve NDEigensystem producing imaginary eigenfrequencies for the vibrations of a cantilever Jan 26 comment HIghlight intersection of two disks It looks to me like the main issue you're after is the same as discussed in the following link: How to embed a filled Region in a Graphics? Jan 26 awarded Yearling Jan 26 reviewed Close Weighted arithmetic mean Jan 26 reviewed Close Workbench error message: LinkObject::linkv: Argument Null in Null is not a valid LinkObject Jan 26 reviewed Close Using Mathematica to derive the PDF of A Cos(x) Jan 26 answered Continuously varying tube radius Jan 26 comment Continuously varying tube radius I did something like that here. Jan 25 comment NIntegrate (Helium Singlet and Triplet) (+1) for taking the effort - this confirms that it's not a Mathematica issue. Jan 24 comment NIntegrate (Helium Singlet and Triplet) The reason why the integrals are equal is because the integrands only differ in the sign under the square, hence in the sign of the cross term. But the cross term integrates to zero. So there seems to be no Mathematica issue here. It boils down to Integrate[Sin[\[Theta]1]Cos[\[Theta]1],{\[Theta]1,0,\[Pi]}]. Jan 24 comment Does PlotLegend lie in a figure? The short answer is no. If you make a plot with legends and type Head[%], it will say Legended instead of Graphics or Graphics3D etc. Jan 23 awarded vector Jan 22 reviewed Close Why doesn't Grid evaluate when I wrap all its arguments in Dynamic? Jan 22 comment vector with conditions/assumptions It's not clear what you're trying to achieve, but how about this: \$Assumptions={g0>0}; g[x_] = Abs[g0 + g1[x]]...? This replaces g by g1 where the Abs would make the expression explicitly non-negative. Depends a lot on where you use this, of course. Also: why does the title talk about vectors?