Truth be known, in my personal circles, I have been talking about the direction both you and Strum have helped me with. I just posted, you both replied. And I too have been learning a lot of things. Lots of deep insight in this thread. Thought provoking stuff!
My inspiration for saying this...
Strum, without knowing the exact 9-point stencil you used I tried to replicate the plot you produced (in Matlab I assume?). Apparently, there is no standard for the 9-point kernel although there is some consensus on the 5-point kernel. Different formulations of the finite difference formulae...
(How did you get your pic to appear inline?)
I notice you are using a 9-point stencil here, while I was using a 5-point stencil (on the rectangular grid, you are taking diagonals into account while I am not). You were also using convolution here?
I needed to take some time to think about this whole thing. The convolution method I was working with has a spectral response. By this I mean mean the finite boundary extents should yield oscillations at the extents, and these are related to the spatial step size. When I initialize my array...
This is not an ideal posting, but I could not ignore your request despite the forum's poor rendering ability (AFAIK).
This will work for 1D or 2D functions (the second block is straight from the textbook for simple ODEs). With some modification, you can use it to solve state-space equations...
Goodness, the code tags don't like tabs. This ruins any formatting that makes the code legible! My simulation length is kinda generated from random parameters (yes, I know... I'm testing stuff:nb)).
I made the video kinda cinematic deliberately. When I work in industry, you need to get the...
Okay... seems like my implementation of the Laplacian has some performance issues.My validation method:
Used a 2D function and computed the symbolic Laplacian so I had a perfect reference: f(x,y) = exp(-x2-y2). This is a single 2D hump centered at (0,0). Most of it vanishes at a distance of 2...
I wanted to make a video of my work in progress, although it is not completely validated and bug free. I put up a temporary YouTube video to share what I have at the moment:
I will still be validating the Laplacian later on among other things.
Is there a way I can paste Python code in this forum? I seem to not be very good at figuring out how to perform basic posting operation. I absolutely don't mind sharing the code. It is basic, but works well for 1D and 2D fields with no modification. With basic modification, you can specify...
Yes it is, and no I did not use sparse encoding as I did not think it was necessary here, the ψ(x,y) (order parameter) matrix is a scalar field.
I implemented the discrete Laplacian operator using a convolutional kernel for my 2D complex scalar field and this is an O(n2) complexity operation...
I will have to review what you suggested in detail, I think I have seen this reference somewhere. Furthermore, I am not familiar with the method you speak so it will be worthwhile to look at this.
At the moment, I am trying to push forward with what I have... I don't know how to upload a...
I can't seem to embed an image, but I did a test on a 2D domain: \frac{dψ}{dt} = ∇ψ:
*** 0.00s to 50.00s in 100 timesteps.
*** -10.00 < x < 10.00, delta_x = 200
*** -10.00 < y < 10.00, delta_y = 200
*** Starting simulation at 2016-06-30 15:51:20.
*** Running ODE solver in array mode.
***...
I'm using Python/NumPy to do the simulation and it has complex variable handling. The RK4 algorithm does not seem to have restrictions on domain, but I tried full separation of real and complex parts as you suggested. Furthermore, I appreciate the simple test cases you suggested and used them...
Yes, it does help. Your equation is the one I want to solve, it seems I could not render my equation correctly (new to BB codes). When I think about it, there are no restrictions on the RK algorithm (ie. no restriction to stay with the real domain). Given that Python can handle complex...
I am looking to numerically solve the (complex) Time Domain Ginzburg Landau Equation. I wish to write a python simulator to observe the nucleation of fluxons over a square 2D superconductor domain (eventually 3D, cubic domain).
I am using a fourth order Runge Kutta solver for this which I made...