# Tag Info

### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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1 vote
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### 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
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### 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 ...
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 ...
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