9
votes
Direct Numerical Simulation of reacting flows
Like WolfgangBangerth, I strongly recommend that you reconsider your motivation (or your supervisor's motivation) for this goal. First, look at Center for Exascale Simulation of Combustion in ...
- 30.1k
9
votes
Accepted
FEM for vector valued problems: reference request
Short answer: Just replicate the vector of interpolation functions into a block-diagonal matrix, as showed e.g. on page 5 in this lecture note.
Detailed answer:
Mathematically oriented texts typically ...
- 697
5
votes
k nearest neighbors dictionary for vectors?
What you're describing is also a critical step in the k-nearest-neighbours method. So no need to reinvent the wheel, we can just look how other people have sped up that algorithm.
I don't know about ...
- 1,266
4
votes
How to compute the Helmholtz decomposition of 2D and 3D vector fields?
The short answer is "It depends".
Certainly, you can try to find the Helmholtz decomposition on your sampled data, and find your irrotational and solenoidal components. However, there are certain ...
- 8,542
4
votes
Direct Numerical Simulation of reacting flows
What you suggest is a multi-year research program. Don't even think about doing this yourself, you will not within several years achieve anything that comes close to the current research. Rather, ...
- 52.4k
4
votes
FEM for vector valued problems: reference request
We can show how it works on the example of linear elasticity. In classical finite elements formulations, on every node, we will have a scalar shape (base) function to which we have associated number ...
- 906
4
votes
In Eigen, can a sparse matrix contain vectors/objects instead of simple scalar values?
Certainly. There are a few things you have to define for your type that are listed on this page in the documentation:
https://eigen.tuxfamily.org/dox/TopicCustomizing_CustomScalar.html
It basically ...
- 1,522
3
votes
Accepted
Algorithm to merge two polygons (using connectivities)?
Easy:
Decompose the polygons into (unoriented) line segments each of which is sorted by vertex index:
$$
A = \{[1,2], [2,3], [3,4], [4,5], [1,5]\},
\\
B = \{ [1,6], [6,7],[7,8],[3,8], [2,3], [1,2]...
- 52.4k
3
votes
How can one produce a proper streamline plot?
You can calculate the stream function yourself, and from it you can draw contours or streamlines of constant $\psi$. Let us assume you are on a two-dimensional incompressible flow
$\mathbf{u}=(u,v,0)^...
- 261
2
votes
Plot vector field in matlab
For plotting, it is easier in my opinion to not use meshgrid if you want to scale the arrows. You have a vector field $(E_X, E_Z)$ and you can simply normalize it like in the code below:
...
- 187
2
votes
Arranging variable ranges into a cell MATLAB
you just need to add output to your min() function, e.g.:
[value, ind] = min(v)
ind is ...
- 137
2
votes
Accepted
Vector characterization of cylinder displacements in a box
You're correct, if the orientational vector is unitary. Otherwise you must calculate the unitary vector in the direction of $\vec{O}_1$ and then perform the projection (just divide by the norm of the ...
- 226
2
votes
Accepted
How to deal with numerical errors in electrostatic field calculations
I will try to answer the part of the question regarding the accuracy of the calculation, which certainly affects all the other things.
Integrals of the type ($T_j$ denoting the $j$th triangle in the ...
- 8,542
2
votes
Accepted
Find representatives of vector-space in set of vectors?
You can think of each vector as a point in your linear space. As such, we can use a simple quadtree/octree-like algorithm to map your points into boxes, with "nearby" vectors assigned to the same or ...
- 663
2
votes
In Lanczos algorithm, can we choose the staring vector to be the first eigenvector of the input matrix A?
Of course you can! The starting vector is completely arbitrary. You'll get breakdown at step 1 if you do though. Be sure to check what it entails.
This will typically happen by a "happy accident&...
- 10k
1
vote
Accepted
Computing excited states using itensor (with DMRG)
For anyone interested in this problem, I found the following solution:
...
- 119
1
vote
Accepted
Solving Vectorial Poisson Equation in FENICS
Ok I will answer my own question:
The problem is in the line solve(L==a,A,bc) which needs to be replaced by solve(a==L,A,bc). ...
- 121
1
vote
Plotting or Visualizing a Higher dimensional vector field
Somehow I have to use t-sne, but I really don't know how.
Since you have a PhD my answer will be brief, it's quite a lengthy subject.
The aim of dimensionality reduction is to preserve as much of ...
- 111
1
vote
Find representatives of vector-space in set of vectors?
Initialize the cluster centers as your subset $V\in X$, where $V=\{x_i\}$. Then run a couple of K-mediods iterations. After that you will see that the certain vectors will come closer, essentially ...
- 2,169
1
vote
Find representatives of vector-space in set of vectors?
Sounds like you want to thin your data where it is dense, and learn the support of your data summarized by data points. If you don't have too many points, you can generate a distance matrix, and prune ...
- 860
1
vote
Accepted
Software/code to extract a solenoidal (a.k.a. divergence-free) field from a 2D vector field numerically
After some searching I found a C/C++ function called project() in the article
'Real-Time Fluid Dynamics for Games' by Jos Stam
http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/GDC03.pdf
I ...
- 141
1
vote
Accepted
two level iterators C++
While I don't state this to be an optimal implementation or one taking into account the all edge cases, below is a sample implementation I put together for your task that can give you an idea of how ...
- 3,788
1
vote
Find a permutation matrix (using the Matlab's function $symrcm$) of a matrix $A(2:end, 2:end)$
From your comment "The plot emphasises expectedly the connections of node 1", I guess that maybe the idea is showing that node 1 is connected not only to a set of nodes that are "one close to the ...
- 10k
1
vote
Efficiently approximating sum of 2-norms
If you just want an approximation to the sum of their norms, you can choose a random sample of $m$ of the indices (i.e., a random set $S \subseteq \{1,2,\dots,N\}$ of size $m$) and compute
$$f(\...
- 370
1
vote
Accepted
Vector and index notation equivalence
Is it possible to tell in index notation whether a vector is a row or column vector, or is that supposed to be clear based on context?
It seems the answer is actually lurking in your question itself ...
1
vote
Accepted
Sparse matrix vector product using PETSC
I assume that you are comparing multiplication with an assembled PETSc matrix with your hand-coded matrix-free method. The latter may indeed be faster, but this could be because no entries of ...
- 839
1
vote
Accepted
Rotate 2D shape around origin in a 3D space
You should take a look at the Wikipedia page on rotation matrices, specifically the section on forming a rotation matrix from an axis and an angle. In your case, you have a vector $\vec{v}$ that you ...
- 4,571
Only top scored, non community-wiki answers of a minimum length are eligible