Community Digest

Top new questions this week:

Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?

I would like to numerically solve the following heat equation problem: $$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$ $$ x \in [ -1, 1 ] \tag 2$$ $$ u(x, 0) = 0 \tag 3$$ $$ u(1, t) = A \sin \Bigg(...

finite-difference parabolic-pde spectral-method heat-transfer chebyshev  
user avatar asked by Nikola Ristic Score of 2
user avatar answered by ConvexHull Score of 3

Solving for $X$ in $\sum_{a,b} b a^T b^T X a = Y$

Suppose I have $k$ pairs of $(a,b)$ where $a$ and $b$ are vectors in $\mathbb{R}^d$, $Y$ is $d\times d$ and I need least squares solution for $X$ in the following $$\sum_{(a,b)}^k b a^T (b^T X a) = Y$...

linear-solver matrix-equations  
user avatar asked by Yaroslav Bulatov Score of 2
user avatar answered by Federico Poloni Score of 2

accuracy problem for a null space calculation on a sparse rectangular matrix

I have been using the QR-based approach on this link to find the null space of rectangular matrices, and possibly sparse matrices, that emerge as a result of some coupling conditions of different ...

linear-algebra svd nullspace qr  
user avatar asked by Umut Tabak Score of 1
user avatar answered by Federico Poloni Score of 3

Numerically computing envelope of Gibbs oscillation

If I numerically compute the envelope of $\sin(\pi t)$ using a Hilbert transform, I obtain exactly what I expect: If I do the same for $\mathrm{sinc}(t)$, still I obtain an envelope which agrees with ...

python fourier-transform  
user avatar asked by user14717 Score of 1
user avatar answered by Yimin Score of 1

Overlap matrix and its inverse matrix

Now, we consider a non-orthonormal basis: $$\mathcal{S}_N=\{|\alpha\rangle,a^\dagger|\alpha\rangle,a^{\dagger 2}|\alpha\rangle,\ldots,a^{\dagger N}|\alpha\rangle\},$$ where $|\alpha\rangle$ is the ...

matrix inverse-problem  
user avatar asked by Young Q Score of 1

Finding the Vector $v$ for a Given Householder Matrix Transformation of Non-Collinear Vectors $a$ and $b$

Consider a vector $v$ in $\mathbb{R}^{n\times1}$. The Householder matrix is defined as follows: $$H(v)=I-\dfrac{2vv^T}{v^Tv}.$$ It can be demonstrated that $H(v)$ is symmetric and orthonormal. The ...

linear-algebra matrix householder orthogonality  
user avatar asked by Ilkay Burak Score of 1
user avatar answered by Lutz Lehmann Score of 1

Greatest hits from previous weeks:

How to get started with OpenFOAM for CFD

I'm looking at using OpenFOAM for solving basic internal flows in CFD. What is the best way to get started, and could anyone please point me to a good online reference to go to with any questions I ...

fluid-dynamics openfoam  
user avatar asked by prrao Score of 20
user avatar answered by tmaric Score of 17

What is pseudo time-stepping?

While reading some literature on PDE solvers I came across the term pseudo time-stepping today. It seems to be a common term, however I failed to find a good definition or an introductionary article ...

pde time-integration  
user avatar asked by Florian Brucker Score of 21
user avatar answered by Aron Ahmadia Score of 21

Meaning of "-0.0" in Python?

We are finding in Python some occasional errors in our coordinate transforms and other similar computations that produce a result of -0.0. What purpose does this ...

python floating-point  
user avatar asked by Chris Ison Score of 13

why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...

linear-algebra matlab matrix  
user avatar asked by Sam Christensen Score of 37
user avatar answered by Brian Borchers Score of 68

The real myth of GPU (specifically CUDA) really speed up FEM/CFD

Now I have been believing that FEM/CFD is supposed to be faster on a GPU unit - here I am using CUDA as solid example. However, I have not been able to find a convincing paper where the benchmark ...

finite-element fluid-dynamics performance cuda  
user avatar asked by Quang Thinh Ha Score of 10
user avatar answered by Chris Rackauckas Score of 21

Visually appealing ways to plot singular vector fields with matplotlib or other foss tools

What is the best way to get a visual appealing plot of a singular vector field (if you want to visualize also the field strength). As an example I am playing with the electric fields of two point ...

python visualization  
user avatar asked by Julia Score of 13
user avatar answered by Henri Menke Score of 8

Periodic boundary condition for the heat equation in ]0,1[

Let us consider a smooth initial condition and the heat equation in one dimension : $$ \partial_t u = \partial_{xx} u$$ in the open interval $]0,1[$, and let us assume that we want to solve it ...

pde boundary-conditions parabolic-pde  
user avatar asked by bela83 Score of 14
user avatar answered by Doug Lipinski Score of 11
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