I am quite new to Julia so I maybe missed the proper documentation.
Is it possible to define a PDESystem in ModelingToolKit with symbolic BCs and Domain for arbitrary geometry?
For instance, if I want to solve the 2D Navier-Stokes equations with a PINN in the following period-hill shape with a curved ground:
How can I defined a no-slip boundary condition on the ground and how can I limit my y-axis to range from y/H = ground(x) to y/H=3 ?
Thanks in advance!
That just doesn't exist right now. The PDESystem parts are still under very active development.
Related
I want to simulate a 2D heat transfer process in the subsurface on a region which is infinite on the r-direction. So, as you know, the very basic way to model this is to draw a geometry that is very long in the r direction. I have done this, and the results that I obtain is correct as in this case, the results are matched with the analytical solution. As you know, there is a capability in Comsol called infinite element domain which serves the purpose to the problem mentioned above. In this case, we need to define a limited geometry on which we want to solve the PDE, and also need to draw a small domain acting as the Infinite Element Domain. However, in this case, the results are not correct because they are not matched with the analytical solution. Is there anything that I am missing to correctly use Infinite Element Domain in comsol?
Any help or comment would be appreciated.
Edit:
I edited the post to be more specific.
Please consider the following figure where a fluid with high temperature is being injected into a region with lower temperature:
https://i.stack.imgur.com/BQycC.png
The equation to solve is:
https://i.stack.imgur.com/qrZcK.png
With the following initial and boundary conditions (note that the upper and lower boundary condition is no-flux):
https://i.stack.imgur.com/l7pHo.png
We want to obtain the temperature profile over the length of rw<r<140 m (rw is very small and is equal to 0.005 m here) at different times. One way to model this numerically in Comsol is to draw a rectangle that is 2000 m in the r-direction, and get results only in the span of r [rw,140] m:
https://i.stack.imgur.com/BKCOi.png
The results of this case is fine, because they are well-matched with the analytical solution.
Another way to model this is to replace the above geometry with a bounded one that is [rw, 140] m in the r-direction and then augment it with an Infinite Element domain that is meshed mapped, as follows:
https://i.stack.imgur.com/m9ksm.png
Here, I have set the thickness of Infinite Element to 10 m in the r-direction. However, the results in this case are not matched with the analytical solution (or the above case where Infinite Element domain was not used). Is there anything that I am missing in Comsol? I have also changed some variables with regard to Infinite Element in Comsol such as physical width or distance, but I didn't see any changes in the results.
BTW, here are the results:
https://i.stack.imgur.com/cdaPH.png
need help on cytoscape as I am starting up using this library but can't get answer on Cytoscape guide.
I created nodes and edges with specific weights.
I'd like to highlight for a given source and target nodes the 2 best paths. First in green and second highlighted in red.
I dont care using Dijkstra, astar, ... as long as it does the job. Both paths could follow same paths if no other choice (example if source node has only 1 connection to its neighbor). in order to filter out edge already used for first path, I create specific data (isPrimary and IsDiverse) in edge such as :
data: { id:'1', source: 'node1', target: 'node2', weight: 0, isPrimary: 0, isDiverse: 0 }. if primary path uses this edge , it will flag isPrimary to True. But cannot be able to make it work.
Do you have concrete example that would do the job as I am stuck since weeks now.
many thx for your supports.
A.
I am assuming that by best path you mean the shortest path.
The problem you describe is known as k-shortest path. Many algorithms have been developed to solve this problem. But unfortunately, as far as I know, none of them is implemented in Cytoscape.js.
Your best bet is to implement Yen's algorithm by utilizing the Dijkstra's algorithm in Cytoscape.js Here is a pseudocode (page 13).
Thx for your answer. I managed to add a parameters (data) onto each edge and flag it as True when used by the best path. Then to find the second best path that should not use the first best path, I create a condition to avoid using edges having flag sets to True.
Here is my problem which I am trying to solve since one complete year. With no success till end of the year. I have to seek help and a concrete solutions from the stackoverflow experts.
My problem statement:
I have been working with some design patterns which I want to trace if eulerian path exist(as shown in below gifs), programmatically. Below are the patterns and the way I wanna draw them(gifs).
What I wanna achieve:
Give the design pattern images as input. I want trace the design pattern image in a single stroke as shown in the gifs(gifs animations are just examples of how the patterns is drawn in single stroke). Once I get the x and y coordinates of the image in single stroke fashion(eulerian path). I will feed those coordinates to my program to just trace those coordinates.
Thing to be noted in the animation:
1) basically its an undetected graph (the nodes being the vertices of your shapes, the edges if exists being the strokes between 2 vertices). (eulerian path)
Here are the 15 unique shapes which I used to build the patterns with:
I have more then 400 patterns(3 patterns already shown below) and till now I am not able to find a generic solution for this. I have manually got the x y coordinates of the patterns and placed it in sequence. But that is not at all scalable.
How to trace the patterns such that each node is visited only once ?:
1st kind of pattern and the way it should be drawn:
2nd kind of pattern and the way it should be drawn:
3rd kind of pattern and the way it should be drawn:
Perhaps you can look into the traveling salesman problem if your still struggling with the above. TSP visits cities only once. And if in your case each node is a crossing for your strike-through then this might help.
Check here for the python code to look at. I've checked and the print statement looks nice and structured. Well done cMinor!
Edit based on discussion: file 1, file2, file3.
I'm working with openCV and I'm a newbie in this field. I'm researching about Camshift. I want to extend this method by using multiple histograms. It means when tracking an object has many than one apperance (ex: rubik cube with six apperance), if we use only one histogram, Camshift will most likely fail.
I know calcHist function in openCV (http://docs.opencv.org/modules/imgproc/doc/histograms.html#calchist) has a parameter is "accumulate", but I don't know how to use and when to use (apply for camshiftdemo.cpp in opencv samples folder). This function can help me solve this problem? Or I have to use difference solution?
I have an idea, that is: create an array histogram for object, for every appearance condition that strongly varies in color, we pre-compute and store all to this array. But when we compute new histogram? It means that the pre-condition to start compute new histogram is what?
And what happend if I have to track multiple object has same color?
Everybody please help me. Thank you so much!
I want to get the properly rendered projection result from a Stage3D framework that presents something of a 'gray box' interface via its API. It is gray rather than black because I can see this critical snippet of source code:
matrix3D.copyFrom (renderable.getRenderSceneTransform (camera));
matrix3D.append (viewProjection);
The projection rendering technique that perfectly suits my needs comes from a helpful tutorial that works directly with AGAL rather than any particular framework. Its comparable rendering logic snippet looks like this:
cube.mat.copyToMatrix3D (drawMatrix);
drawMatrix.prepend (worldToClip);
So, I believe the correct, general summary of what is going on here is that both pieces of code are setting up the proper combined matrix to be sent to the Vertex Shader where that matrix will be a parameter to the m44 AGAL operation. The general description is that the combined matrix will take us from Object Local Space through Camera View Space to Screen or Clipping Space.
My problem can be summarized as arising from my ignorance of proper matrix operations. I believe my failed attempt to merge the two environments arises precisely because the semantics of prepending one matrix to another is not, and is never intended to be, equivalent to appending that matrix to the other. My request, then, can be summarized in this way. Because I have no control over the calling sequence that the framework will issue, e.g., I must live with an append operation, I can only try to fix things on the side where I prepare the matrix which is to be appended. That code is not black-boxed, but it is too complex for me to know how to change it so that it would meet the interface requirements posed by the framework.
Is there some sequence of inversions, transformations or other manuevers which would let me modify a viewProjection matrix that was designed to be prepended, so that it will turn out right when it is, instead, appended to the Object's World Space coordinates?
I am providing an answer more out of desperation than sure understanding, and still hope I will receive a better answer from those more knowledgeable. From Dunn and Parberry's "3D Math Primer" I learned that "transposing the product of two matrices is the same as taking the product of their transposes in reverse order."
Without being able to understand how to enter text involving superscripts, I am not sure if I can reduce my approach to a helpful mathematical formulation, so I will invent a syntax using functional notation. The equivalency noted by Dunn and Parberry would be something like:
AB = transpose (B) x transpose (A)
That comes close to solving my problem, which problem, to restate, is really just a problem arising out of the fact that I cannot control the behavior of the internal matrix operations in the framework package. I can, however, perform appropriate matrix operations on either side of the workflow from local object coordinates to those required by the GPU Vertex Shader.
I have not completed the test of my solution, which requires the final step to be taken in the AGAL shader, but I have been able to confirm in AS3 that the last 'un-transform' does yield exactly the same combined raw data as the example from the author of the camera with the desired lens properties whose implementation involves prepending rather than appending.
BA = transpose (transpose (A) x transpose (B))
I have also not yet tested to see if these extra calculations are so processing intensive as to reduce my application frame rate beyond what is acceptable, but am pleased at least to be able to confirm that the computations yield the same result.