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1500 questions
7
votes
2 answers
Bin-packing: Maximise number of bins / "Fukubukuro" problem?
I recently encountered a problem that looks like a variation of bin packing or knapsack problem, but with the objective to maximise the number of bins/knapsacks:
Consider there is a list of M items with positive values v1 to vM respectively. There…
peterwhy
- 171
- 3
7
votes
2 answers
Evaluation of Vandermonde matrix
I would like to construct a Finite Element basis by using a generalized Vandermonde matrix. The idea is to compute the values of a suitable modal basis ('prime basis') at a set of points in reference space and express the values of Finite Element…
Martin Vymazal
- 405
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7
votes
2 answers
ODE: How to measure stiffness if the Jacobian has zero eigenvalues?
Say you have a system of ODE's where the Jacobian has one zero eigenvalue; what does that tell you about the stiffness of the system?
This case doesn't seem to be discussed in the cases I have been able to find (Stiffness ratio or stiffness index).
trolle3000
- 315
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7
votes
1 answer
Full Multigrid Prolongation Operator
I am looking into full multigrid, FMG, and several sources, including these slides, that a lot of people are referring to, state that the prolongation operator used in FMG the first time you visit a finer grid should be of higher order than the…
Gunnhild
- 71
- 1
7
votes
2 answers
How do I solve a boundary value ODE in MATLAB?
Specifically, ode15i. I have ode15i solving a system of 5 first order implicit odes in 5 variables with an initial condition (made consistent by decic). It's great for what I need, except I need to add a final condition as well. Is this possible? I…
Samuel Reid
- 173
- 6
7
votes
3 answers
Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?
In Theorem 6.2 of their 2003 paper on "Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal., 40(6), 2171–2194", D. Schötzau, Ch. Schwab, and A. Toselli prove a bound of the $\inf$-$\sup$ constant of the Stokes problem which decreases by…
Guido Kanschat
- 1,124
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7
votes
2 answers
Hartree Fock iteration problem
I am writing a program to compute the ground state energy for any closed shell atom using Hartree Fock Roothaan method, with GTO basis. The code works for the simplest case, the helium, but it fails with beryllium (z=4).
I understand that I have two…
Cheong
7
votes
2 answers
Convergence of adaptive finite elements with inexact solves
I'm working on some adaptive discontinuous Galerkin codes for time harmonic wave propagation, currently just Helmholtz, but will be branching out once I have a working prototype in this case.
There are some papers out there demonstrating that…
Reid.Atcheson
- 3,283
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7
votes
2 answers
Sparse Incomplete Cholesky
I'm looking for an efficient, multicore, library to do incomplete cholesky (possibly modified). Many ILU code exists, but I can't find much about IC except in PETSC or Pastix. Could some of you drop me any library name ?
Thank you !
Tom
Tom
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7
votes
1 answer
Navier-Stokes solver: How to adjust the time step based on non-linear terms?
My code solves the incompressible Navier-Stokes equation in a conducting fluid, together with the induction equation:
$ \partial_t u + u \nabla u + 2\Omega \times u = -\nabla p + \nu \Delta u + (\nabla \times b) \times b \\
\partial_t b = \nabla…
nat chouf
- 353
- 2
- 10
7
votes
1 answer
A simple question about 1D finite element derivatives
For 1D derivative we have
\begin{equation}
F(x) = \frac{\partial f(x)}{\partial x}
\end{equation}
\begin{equation}
f(x)=\sum_{i}f_ie_i(x)
\end{equation}
\begin{equation}
F(x)=\sum_{i}F_ie_i(x)
\end{equation}
where…
yangjinhui
- 71
- 1
7
votes
2 answers
Is there a fast way to compute histograms for high-dimensional large datasets?
Currently the way I compute histograms for data is by generating grid in $N$ dimensions (where $N$ is the dimension of the data) and searching through the $M$ data points in each dimension to see in which bin each one of them fits.
This is the same…
Ron
- 265
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7
votes
2 answers
How to numerically solve a laser driving semi-classical two-level system using Floquet formalism?
Consider the semi-classical laser driving two-level atom, where the laser is treated classically and the atom is treated quantum mechanically. The effect of laser on the atom is a dipole…
xslittlegrass
- 345
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7
votes
1 answer
Potential flow around a non-symmetric obstacle using stream functions
I've seen that there is a way to use the finite differences method, on a cartesian orthogonal grid, to perform calculations on potential flow about an obstacle without using the Neumann conditions, but only Dirichlet conditions. It is done using the…
john
- 71
- 1
7
votes
2 answers
FEniCS: boundary conditions for electrostatic problems with dielectrics
I carefully read all circa 70 pages of FEniCS tutorial and I still do not understand how to solve electrostatic problems when I have materials with different dielectric constant. The self contained system of equations in…
facetus
- 358
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