Top new questions this week:
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This question is neither scientific nor technical but more career related.
I am at a junction in my professional life where I need to make a decision with regard to the future of my career. At the ...
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Engineering FEM
When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as:
Multiply your PDE with a test ...
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This is a continuation of my previous question. I am trying to effectively compute a bound for the roundoff errors in some FEM computation (2d polygons, triangular meshes). Below I will write some of ...
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I have been using Pointwise for grid generation and found the quality of smoothed grids to be stunning.
I am not aware of any free/open source alteranative that offers the same capabilities for ...
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To compute the $N$-point DFT
$$ X[k] = \sum_{n=0}^{N-1} x[n] W_N^{kn} $$
where $N = N_1 N_2$, we can write the indices as $n = N_2 n_1 + n_2$ and $k = k_1 + N_1 k_2$, (effectively packing the data ...
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I'm implementing a solver of Finite Element Method, and to solve the linear system of equations I'm using gmres from MKL of Intel. Exists the option with and without a preconditioning. In what case it ...
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I often hear that cell centred finite volume is second order accurate but at the same time I come across notions of high order FVM flux schemes. Is there a distinction between the two? If I were to ...
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Greatest hits from previous weeks:
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So I've got a decent head for what problems I work with are best one in serial, and which can be managed in parallel. But right now, I don't have much of an idea of what's best handled by CPU-based ...
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Given is an increasing finite sequence of positive numbers $z_{1} ,z_{2},.....z_{n}$. Which of the following two algorithms is better for computing the sum of the numbers?
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This question is an extension of two discussions that came up recently in the replies to "C++ vs Fortran for HPC". And it is a bit more of a challenge than a question...
One of the most often-heard ...
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The advection equation needs to be discretized in order to be used for the Crank-Nicolson method. Can someone show me how to do that?
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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 ...
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I'm considering learning a new language to use for numerical/simulation modelling projects, as a (partial) replacement for the C++ and Python that I currently use. I came across Julia, which sounds ...
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What can go wrong when using preconditoned Krylov methods from KSP (PETSc's linear solver package) to solve a sparse linear system such as those obtained by discretizing and linearizing partial ...
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Can you answer these questions?
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I'm following this low-pass filter example in the text "Image Operators: Image Processing in Python 1st Edition" by Jason M. Kinser, but can't seem to duplicate their results.
The text's ...
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I do a lot of 2D discrete FFT in python using np.fft.fftshift(np.fft.fft2(y)), then throw away 90% or more of the array, keeping only the central low-frequency area....
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Consider the following differential equation
\begin{align}
\frac{\partial f(u)}{\partial x} &= g(x), \ \ x\in [x_{L},x_{R}] \label{Eq2.2} \\
u(x_{L}) &= g_{1}
\end{align}
where $f(u)$ is a ...
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