Computational Science Stack Exchange
Computational Science Stack Exchange

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1500 questions
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3 answers

Is variable scaling essential when solving some PDE problems numerically?

In semiconductor simulation, it is common that the equations are scaled so they have normalised values. For example, in extreme cases electron density in semiconductors can vary over 18 order of magnitude, and electric field can change shapely, over…
boyfarrell
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What is the fastest way to compute all eigenvalues of a very big and sparse adjacency matrix in python?

I'm trying to figure out if there is a faster way to compute all the eigenvalues and eigenvectors of a very big and sparse adjacency matrix than using scipy.sparse.linalg.eigsh As far as I know, this methods only uses the sparseness and symmetry…
Noam Peled
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Why does SciPy eigsh() produce erroneous eigenvalues in case of harmonic oscillator?

I'm developing some larger code to perform eigenvalue computations of huge sparse matrices, in the context of computational physics. I test my routines against the simple harmonic oscillator in one dimension, since the eigenvalues are well known…
seb
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Python OSS alternatives for Matlab Neural Network Toolbox. Any intercomparisons?

I'd like to be independent of commercial software for my scientific work. I find a dependence an commercial packages such as Matlab and its toolboxes unsatisfactory, because I do not know if I will have access to Matlab in the future, and because I…
gerrit
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multigrid method to solve PDE

I need simple explanation of the Multigrid Method or some literature about this. I am familiar with iterational methods including BiCGStab,CG,GS,Jacobi and preconditioning, but I am a beginner with multigrid method. Can someone explain this in…
Nurlan
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4 answers

uniform vs. non-uniform grid

It is probably a student level question but I can't exactly make it cleat to myself. Why is it more accurate to use non-uniform grids in the numerical methods? I am thinking in the context of some finite-difference method for the PDE of the form…
Kamil
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7 answers

Does Computational Science involve programming?

I read about computational science on Wikipedia, but my understanding is not very clear. Does computational science involve programming? How different is computational science from computational _____, where the blank could be any discipline…
Sheryl
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16
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2 answers

Estimation of condition numbers for very large matrices

Which approaches are used in practice for estimating the condition number of large sparse matrices?
Allan P. Engsig-Karup
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2 answers

Open source implementation of rational approximation to a function

I am looking for some open source implementation (any of Python, C, C++, Fortran is fine) of rational approximation to a function. Something along the article [1]. I give it a function and it gives me back two polynomials, whose ratio is the…
Ondřej Čertík
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How can I estimate the condition number of a large sparse matrix using PETSc?

I have a PETSc Mat and would like to estimate its condition number.
Jed Brown
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Numerical methods for discontinuous r.s. ODEs

what are state of art methods for numerical solution of ODEs with discontinuous right side? I'm mostly interested piecewise-smooth right side functions, e.g. sign. I'm trying to solve the equation of a following type: \begin{align*} \dot x &=…
Andrey Shevlyakov
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Boost::mpi or C MPI for high performance scientific applications?

The thing I dislike most about MPI is dealing with datatypes (i.e. data maps/masks) because they don't fit that nicely with object oriented C++. boost::mpi only supports MPI 1.1, however, from their website: boost::mpi is a C++ friendly interface…
gnzlbg
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6 answers

Example of a continuous function that is difficult to approximate with polynomials

For teaching purposes I'd need a continuous function of a single variable that is "difficult" to approximate with polynomials, i.e. one would need very high powers in a power series to "fit" this function well. I intend to show my students the…
András Aszódi
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What is counterpoise correction?

What is counterpoise correction exactly ? Can you explain when it is needed and why ?
Stefano Borini
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How should I study creating and programming HPC systems?

I'm in a field that doesn't necessarily do a great deal of HPC work, and when it does encounter it, it's often the result of researchers from other fields exploring new applications to their methods and the like. Primarily what this means is that it…
Fomite
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