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1500 questions
30
votes
4 answers
Is half precision supported by modern architecture?
I am new to computer science and I was wondering whether half precision is supported by modern architecture in the same way as single or double precision is. I thought the 2008 revision of IEEE-754 standard introduced both quadruple and half…
Asad Mehasi
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30
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9 answers
What is a good way to run parameter studies in C++
The problem
I'm currently working on a Finite Element Navier Stokes simulation and I would like to investigate the effects of a variety of parameters. Some parameters are specified in an input file or via a command line options; other parameters are…
Matija Kecman
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30
votes
7 answers
Where do the laws of quantum mechanics break down in simulations?
As someone who holds a BA in physics I was somewhat scandalized when I began working with molecular simulations. It was a bit of a shock to discover that even the most detailed and computationally expensive simulations can't quantitatively reproduce…
tel
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30
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5 answers
Are there any famous problems/algorithms in scientific computing that cannot be sped up by parallelisation
Are there any famous problems/algorithms in scientific computing that cannot be sped up by parallelisation? It seems to me whilst reading books on CUDA that most things can be.
RNs_Ghost
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30
votes
3 answers
What is the principle behind the convergence of Krylov subspace methods for solving linear systems of equations?
As I understand it, there are two major categories of iterative methods for solving linear systems of equations:
Stationary Methods (Jacobi, Gauss-Seidel, SOR, Multigrid)
Krylov Subspace methods (Conjugate Gradient, GMRES, etc.)
I understand…
Paul
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29
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3 answers
What is the purpose of using integration by parts in deriving a weak form for FEM discretization?
When going from the strong form of a PDE to the FEM form it seems one should always do this by first stating the variational form. To do this you multiply the strong form by an element in some (Sobolev) space and integrate over your region. This I…
Christian
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29
votes
1 answer
Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation
I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle density) under diffusion and advection. Particle density…
boyfarrell
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29
votes
4 answers
Dealing with the inverse of a positive definite symmetric (covariance) matrix?
In statistics and its various applications, we often calculate the covariance matrix, which is positive definite (in the cases considered) and symmetric, for various uses. Sometimes, we need the inverse of this matrix for various computations…
Benjamin Allévius
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29
votes
5 answers
Fastest Delaunay triangulation libraries for sets of 3D points
Which is the fastest library for performing delaunay triangulation of sets with millions if 3D points? Are there also GPU versions available? From the other side, having the voronoi tessellation of the same set of points, would help (in terms of…
Open the way
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29
votes
2 answers
Does a tiny determinant imply ill-conditioning of a matrix?
If I have a square invertible matrix and I take its determinant, and I find that $\det(A) \approx 0$, does this imply that the matrix is poorly conditioned?
Is the converse also true? Does an ill-conditioned matrix have a nearly zero…
Inquest
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29
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10 answers
Fast, lightweight C++ tensor library for dimension-agnostic code
I am looking for a C++ tensor library that supports dimension-agnostic code. Specifically, I need to perform operations along each dimension (up to 3), e.g. calculating a weighted sum. The dimensions is a template parameter (and thus a compile-time…
Michael Schlottke-Lakemper
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28
votes
3 answers
What's the state-of-the-art in highly oscillatory integral computation?
What's the state-of-the-art in the approximation of highly oscillatory integrals in both one dimension and higher dimensions to arbitrary precision?
Quadrescence
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28
votes
3 answers
BFGS vs. Conjugate Gradient Method
What considerations should I be making when choosing between BFGS and conjugate gradient for optimization? The function I am trying to fit with these variables are exponential functions; however, the actual objective function involves integration,…
drjrm3
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28
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5 answers
What are the main differences between PETSc and Trilinos?
As far as I can tell, the two big generic US Department of Energy computational science software frameworks are PETSc and Trilinos. They seem similar at first glance, beyond differences in language (C versus C++). What are the main differences…
Geoff Oxberry
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28
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4 answers
The easiest way to find intersection of two intervals
Right now I stuck with a problem. It seems to be really trivial one, but still it is hard for me to find an appropriate solution. The problem is:
One has two intervals and are to find the intersection of them.
For instance:
Intersection of [0,…
some1 here
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