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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?