# Computational Science Stack Exchange Community Digest

## Top new questions this week:

### Which algorithms(paper) should be reproduced by a student to enter the field of computational fluid-structure interaction?

We'd better not to reinvent the wheel. But without some programming, one can hardly understand computational fluid-structure interaction. And I would like to know which papers or algorithms should a ...

algorithms multiphysics fsi asked by Dong Ivan 4 votes answered by Chenna K 1 vote

### When does L-BFGS outperform GD?

In practice, L-BFGS is frequently held comparably to other inexact QN methods, and it provides a middle ground of sorts between Hestenes–Stiefel CG and BFGS as memory goes from zero to infinity (...

convergence quasi-newton asked by VF1 4 votes

### Guidelines for publishing data from a stochastic simulation

So, my question is if one should ideally keep a record of all seeds that are used when publishing numerical work that involves one or more random number generators (e.g. a stochastic simulation), and ...

stochastic publications asked by TLDR 4 votes answered by Brian Borchers 3 votes

### Optimize linear equation using inner products and subject to L1 norm

I have a linear system of the form $A x = b$ where $A$ and $b$ are known, $A$ is "square", and $\lvert b \rvert_1 = \lvert x \rvert_1 = 1$. Unfortunately, I am working in a framework that ...

linear-algebra optimization asked by emprice 4 votes

### Is upwinding needed for slope limiter / flux limiter and numerical flux?

I have a cell centered cartesian grid and am trying to implement the flux inside the divergence term using numerical flux with a flux limiter. I found different formulas for MUSCL flux limiter, where ...

finite-volume asked by Emil 3 votes

### Hack for using hardware to take square roots of 128 bit numbers

I need to take integer square roots $\lfloor \sqrt{n}\rfloor$ of (lots of) 128 bit numbers $n$. Calling gmp seems to take surprisingly long (though I can't tell for sure, since gmp routines are not ...

floating-point asked by H A Helfgott 2 votes answered by njuffa 1 vote

I am taking a computational linear algebra course and i got stuck during a homework problem concerning the computation of inner products. I am supposed to compute the inner product:$$\mathrm{a}_{\... linear-algebra numerics symbolic-computation asked by Lucas 2 votes ## Greatest hits from previous weeks: ### How to find more than one root of a polynomial? This program finds the first root of the function f, defined in the code. There are 5 roots of this function. (x=1,2,3,4,5) I wish to find all of the roots in this program and print them to the screen.... c++ polynomials nonlinear-equations roots asked by flamingohats 7 votes ### How do I take the FFT of unevenly spaced data? The Fast Fourier Transform algorithm computes a Fourier decomposition under the assumption that its input points are equally spaced in the time domain, t_k = kT. What if they're not? Is there ... fourier-analysis asked by David Z 59 votes answered by Jack Poulson 44 votes ### scipy.optimize.fmin_bfgs: "Desired error not necessarily achieved due to precision loss" I am getting the warning in the post subject when attempting to optimize a function in Python with the scipy.optimize.fmin_bfgs function. The complete output: Warning: Desired error not necessarily ... optimization python asked by ACEG 8 votes answered by Aron Ahmadia 10 votes ### Define custom probability density function in Python Is there a way, using some established Python package (e.g. SciPy) to define my own probability density function (without any prior data, just f(x) = a x + b), so I can then make calculations with ... python statistics probability asked by astrojuanlu 23 votes answered by GertVdE 26 votes ### Intel Fortran Compiler: tips on optimization at compilation 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.... performance hpc compiling fortran asked by FrenchKheldar 22 votes answered by OscarB 6 votes ### CUDA vs OpenCL as of late 2013 How do CUDA and OpenCL compare to each other as of late 2013 from a programmer's perspective? My group is thinking about trying to make use of GPU computing. Would we be limiting ourself ... hpc gpu cuda opencl asked by Szabolcs 34 votes answered by Karl Rupp 37 votes ### Concave polygon 'hull' finding I implemented an algorithm to find the alpha shape of a set of points. The alpha shape is a concave hull for a set of points, whose shape depends on a parameter alpha deciding which points make up the ... algorithms computational-geometry graph-theory convex-hull asked by kiriloff 6 votes ## Can you answer these questions? ### Multigrid Reduction In Time Convergence I am trying to solve a 2D dynamic linear elasticity model parallel in time using Xbraid. The spatial domain is [0,1]x[0,1] and time domain [0,1]. For time integration I am using a backward Euler ... parallel-computing convergence time-integration multigrid parallel-in-time asked by spyros 1 vote ### Explicit DG time step restriction for compressible Navier-Stokes equations Hesthaven's book 1 mentions the following time step restriction for Navier-Stokes equations (see (7.32) in 2008 edition)$$ \Delta t \approx \frac{h}{N^2} \frac{C}{|u| + |c| + \frac {N^2 \mu}{h}}  (\$...

time-integration navier-stokes discontinuous-galerkin asked by Zxcvasdf 1 vote
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