Top new questions this week:
|
|
I would like to numerically solve the following heat equation problem:
$$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$
$$ x \in [ -1, 1 ] \tag 2$$
$$ u(x, 0) = 0 \tag 3$$
$$ u(1, t) = A \sin \Bigg(...
|
|
Suppose I have $k$ pairs of $(a,b)$ where $a$ and $b$ are vectors in $\mathbb{R}^d$, $Y$ is $d\times d$ and I need least squares solution for $X$ in the following
$$\sum_{(a,b)}^k b a^T (b^T X a) = Y$...
|
|
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 ...
|
|
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 ...
|
|
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 ...
|
|
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 ...
|
Greatest hits from previous weeks:
|
|
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 ...
|
|
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 ...
|
|
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 ...
|
|
$A$ 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,...
|
|
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 ...
|
|
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 ...
|
|
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 ...
|
