Top new questions this week:
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I am using interior penalty discontinuous Galerkin to solve a simple Laplace problem: \begin{align*} \nabla u=0 \end{align*} with prescribed 0 and 1 Dirichlet boundary conditions on opposite edges of …
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Consider a convex polygon in $\mathbb{R}^2$ with multiple convex holes in it and suppose that, for now, we have a 2D triangular mesh of the polygon, which is represented by $\mathcal{T} \equiv\{T_i\}…
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In FEM with bubble functions, the field ($\boldsymbol{u}$) is approximated as a linear combination of the standard one ($\tilde{\boldsymbol{u}}$) plus the bubble field ($\boldsymbol{u}^b$). That is, \…
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Greatest hits from previous weeks:
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I have a simple question that is really hard to Google (besides the canonical What Every Computer Scientist Should Know About Floating-Point Arithmetic paper). When should functions such as …
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Recently, I’ve encountered a bizarre problem with FORTRAN95. I initialized variables X and Y as follows: X=1.0 Y=0.1 Later I add them together and print the …
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Suppose I’m using a linear congruential pseudo-random number generator (PRNG). Given a seed $x_0$, the multiplying factor (a), the shift factor (c) and the modulus factor (m), how can I determine the …
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I want to plot a numerical integral function of some function $f$ using scipy and matplotlib. How can I do this? I tried the …
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Given two computational programs, one using a Gaussian basis, and the other using Slater basis, what are the practical differences, advantages and disadvantages for each choice ?
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I will start with my personal experience in our lab. Back in the ifort 9 and 10 days, we used to be quite aggressive with the optimizations, compiling with -O3 and processor specific flags (-xW -xSSE4….
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If a matrix $A_{n\times n}$ is invertible, then $\left\|A^{-1}\right\|_2 = \dfrac{1}{\min\limits_{i} \sigma_i}$ where $\sigma_i$ is the $i$-th singular value of $A$
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