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1500 questions
8
votes
5 answers
Choice of basis in FEM
Briefly, what are the different types of basis used in FEM and why is the nodal basis so popular and advantageous in the finite element context?
kfkhalili
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8
votes
2 answers
discrete definitions of curl $\nabla \times F$?
I have some data defined in an array (an image) and I need to find the curl of a certain function.
Wikipedia has an integral definition of curl that I like, maybe it can be discrete.
$$ \nabla \times F = \frac{1}{|A|} \oint F \cdot d…
john mangual
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8
votes
2 answers
Name of an Optimization Approach to Reduce Size of Variable Space
I am dealing with an optimization problem that has a large number of variables to optimize over - for example let's call these variables $x$, $y$, and $z$ and I wish to minimize the function $f(x,y,z)$. The optimization method that I am using is not…
user69813
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- 4
8
votes
2 answers
Intel Knights Landing work loads vs NVIDIA GeForce
There are lot of articles being written about how the newly launched Intel Xeon Phi will steal the HPC\Super Computer market share from the competitors. Intel Knights is equipped with 72 cores and 4 sockets making it 288 core system. Whereas a…
Chandan
- 183
- 4
8
votes
0 answers
DIIS method to accelerate SCF convergence for stretched geometries
I am implementing from scratch an Hartree-Fock calculation in the STO-3G basis set to perform Born-Oppenheimer molecular dynamics. I have a Restricted Hartree-Fock procedure that can reproduce very well the total energies of Ref. [1] and of…
user18279
8
votes
1 answer
Implementation of LP with separation oracle?
I'm looking for an implementation of the ellipsoid algorithm for linear programming since the application I have in mind has the constraints represented as a separation oracle. Is such an implementation available anywhere?
If there isn't, is there…
G. Bach
- 183
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8
votes
2 answers
Sum over very small exponentials: Underflow
I am trying to compute (in C) a sum like
$S = \sum_i \exp( - a_i )$,
where $10^{4} < a_i < 10^{5}$ are approximately normal distributed. So even if I do the Log-Sum-Exp trick
$S = \exp(\log[\sum_i \exp( - a_i + K )] - K)$,
with $K = \min_i(a_i)$,…
fastfforward
- 83
- 4
8
votes
1 answer
Fast computation of component-wise $\exp(-XY^T)G$ for random $G$
I have the following question:
Suppose I have two matrices $X, Y$ both of size $m\times p$ and a random i.i.d Gaussian matrix $G$ of size $m \times k$, $m\gg p>k$.
Is there a fast way to compute $\exp(-XY^T)G$? Perhaps by using the fact that both…
Gil
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8
votes
1 answer
How can I compute the Schur complement in PETSc?
How can I compute the Schur complement:
$$ S = K_{bb} - K_{ba} K_{aa}^{-1} K_{ab} $$
where
$$ K=\begin{pmatrix} K_{aa} & K_{ab} \\ K_{ba} & K_{bb} \end{pmatrix} $$
(in some ordering) is a PETSc matrix (Mat)?
Peter Brune
- 1,675
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8
votes
3 answers
Good introduction to numerical methods for magnetohydrodynamics (MHD)
I very recently started to read up about magnetohydrodynamics (MHD). While I have experience in the fluid part (both theory and numerics), my knowledge about the magneto part is very limited.
At the moment, I am working through the book by Davidson…
Daniel
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- 10
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8
votes
1 answer
Numerical solution of Geodesic differential equations with Python
I have made a solver based on the SymPy.diffgeom library, where I use Scipy.Integrate to solve the following system of second order differential equations :
\begin{align}
u'' &+ \Gamma^0_{00}(u')^2 + 2\Gamma^0_{01}u'v' + \Gamma^0_{11}(v')^2 = 0,\\…
imranal
- 425
- 3
- 13
8
votes
2 answers
Matrix free finite elements method for visualization in process tomography
I am Computer Scientist and now I am interested in matrix multiplication on GPUs. My research are focused on matrix free finite elements method where I multiply sparse matrix. Sparse matrix could multiply regular or matrix free. In general based on…
Konrad
- 95
- 4
8
votes
1 answer
Difference between Gauss-Newton method and quasi-Newton method for optimization
Can anybody help me? I heard that Gauss-Newton method compute an aproximation of the Hessian instead of the true Hessian, but, quasi-Newton method too, don't it? what is the differences between them?
any help would be appreciated :)
mario faixat
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8
votes
0 answers
Accelerated convergence for Sparse NMF
In the Non-Negative Matrix factorization (NMF), you basically compute an approximation of a given matrix $V \in \mathbb{R}_{+}^{n \times m}$ into matrices $W$ and $H$ such that $W \in \mathbb{R}_{+}^{n \times r}$ and $H \in \mathbb{R}_{+}^{r \times…
Gilles
- 253
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8
votes
2 answers
FEM: Possible to have boundary conditions "inside" the domain?
I work on geological problems and I use the Finite Element Method. But this question can be applied on other classical mechanical problems.
I work on implicit 3D surfaces (which represent the limits between two geological layers aka two media).
I…
AntoineMazuyer
- 95
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