Community Digest

Top new questions this week:

What can a computational scientist do in the fourth industrial revolution?

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 ...

career-development industry4.0 computational-science-careers  
asked by Dude 9 votes
answered by Biswajit Banerjee 15 votes

FEM : energy minimization VS PDE solving

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 ...

finite-element optimization pde simulation computer-vision  
asked by Txnda 6 votes

Roundoff errors in FEM computations - generalized eigenvalues

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 ...

finite-element eigenvalues error-estimation  
asked by Beni Bogosel 4 votes
answered by user7440 1 vote

Is there any reliable free/open source tool for structured mesh smoothing?

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 ...

mesh-generation grid smoothing  
asked by Pet but Ape 3 votes

3D Cooley-Tukey FFT

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 ...

asked by Brian 3 votes

When do not use preconditioners for sparse linear system of equations?

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 ...

iterative-method preconditioning linear-system gmres  
asked by yemino 3 votes
answered by Anton Menshov 11 votes

What determines the order of a finite volume scheme?

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 ...

asked by CuteCompute 3 votes

Greatest hits from previous weeks:

What kinds of problems lend themselves well to GPU computing?

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 ...

asked by Fomite 89 votes
answered by Max Hutchinson 66 votes

Which algorithm is more accurate for computing the sum of a sorted array of numbers?

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? ...

algorithms floating-point  
asked by CryptoBeginner 24 votes

How much better are Fortran compilers really?

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 ...

fortran c blas benchmarking  
asked by Pedro 78 votes
answered by Jack Poulson 37 votes

How to discretize the advection equation using the Crank-Nicolson method?

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?

pde advection crank-nicolson  
asked by pandoragami 8 votes
answered by boyfarrell 20 votes

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  
asked by bela83 14 votes
answered by Doug Lipinski 10 votes

How mature is the "Julia" scientific computing language project?

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 ...

parallel-computing languages julia  
asked by Nathaniel 59 votes
answered by Chris Rackauckas 56 votes

Why is my iterative linear solver not converging?

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 ...

linear-algebra petsc preconditioning krylov-method iterative-method  
asked by Jed Brown 28 votes

Can you answer these questions?

How do you correctly implement Scipy's FFT procedures to produce a low-pass filter - image processing

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 ...

python scipy fourier-transform image-processing  
asked by Lagreeni 1 vote

2D DFT for lower frequencies only; is there something significantly faster than numpy.fft.fft2 (throwing away high frequencies)?

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....

python fourier-transform  
asked by uhoh 1 vote

Is it possible to use a fixed point iteration for solving this nonlinear system?

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 ...

nonlinear-equations discontinuous-galerkin fixed-point  
asked by TheComander 1 vote
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