All Questions
11,504
questions
9
votes
0
answers
168
views
What's the most computationally efficient implementation of Kalman Filter
I know there are many formulations of the Kalman Filter. A few I can name are:
Classical Covariance Form
Informational Filter Form
Square-Root Form or Factor Form
But somehow it's hard for me to ...
- 425
2
votes
1
answer
158
views
How to add damped constraint force to constrained dynamics simulation?
I have implemented a constraint dynamics physics simulation as proposed by Andrew Witkin et al 1990, but I cannot get the initial constraint "snapping" correctly.
I implemented
$$ JWJ^{T} \...
- 71
1
vote
1
answer
130
views
Coupled Partial Differential Equations
I'm trying to solve the following system of coupled differential equations, the two-temperature model for $e$ = electrons and $l$ = lattice.
$$
\rho_{e}C_{p,e}\frac{\partial T_{e}}{\partial t} = k_{e}\...
- 11
0
votes
1
answer
81
views
optimize this python code that involves matrix inversion
So I have this line of code that involves a matrix inversion
X = A @ B @ np.linalg.pinv(S)
$A$ is an $n$ by $n$ matrix, $B$ is an $n$ by $m$ matrix and $S$ is an $...
- 127
0
votes
1
answer
77
views
GMRES implementation does not converge for singular Hermitian problems
I've just implemented the GMRES algorithm based on chapter 4 of Fundamentals of Numerical Mathematics for Physicists and Engineers using the problems in Numerical Analysis by Timothy Sauer for ...
- 317
1
vote
0
answers
11
views
Guidelines for image detection model for statis sample
I have 20,000 plus images of art (paintings, sculptures, jars, etc). My goal is creating a computer vision model that, from an input (image), identifies the exact same piece of art and returns its id, ...
0
votes
0
answers
69
views
How can I get more accurate electric scalar potential in 2D closed box?
I am trying to use poisson equation to plot the electric scalar potential in close 2D space. The details in in this video
and this one
The following in written in Matlab for quick prototype.
...
- 101
3
votes
0
answers
118
views
Quantifying the inefficiency of Gauss–Hermite quadrature
I am trying to understand the following part of the paper https://doi.org/10.1137/20M1389522 where the author argues about the inefficiency of Gauss-Hermite quadrature.
I think I get the gist of the ...
- 31
2
votes
1
answer
278
views
Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation
I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units):
\begin{align}
i \frac{\...
- 21
0
votes
0
answers
38
views
Split RAM asked between nodes and different partitions
I'm using a Slurm-based HPC at my university to run memory-intensive software. I need to know if it's possible to distribute the required RAM across multiple nodes and partitions. My lab has exclusive ...
- 1
1
vote
1
answer
204
views
Boundary Conditions on the Inlet and Outlet in a Discontinuous Galerkin framework
In the book Discontinuous Galerkin Method (DGM), Analysis and Applications to Compressible Flow by Vít Dolejší and Miloslav Feistauer, Springer, it is mentionned, in section 8.3.2 that deals with ...
- 37
0
votes
0
answers
36
views
Solving for expectation using iteration in a implicit function
For a implicit function $V(k,l)$, taking $l$ as given and $k$ to be the only variable, $k$ is sampling from an unknown distribution and $\mathbb{E}k = \bar{K}$. Using Taylor expansion on $V(k,l)$ ...
- 55
4
votes
1
answer
102
views
How can I efficiently find an anti-symmetric generator of a special orthogonal matrix?
Given a special orthogonal matrix $O$ (i.e: $OO^T = 1$ and $\det(O) = 1$), I am trying to efficiently find a matrix $X$ such that $O = e^X$ and $X = -X^T$ using Python (NumPy & SciPy).
One obvious ...
- 227
1
vote
0
answers
74
views
Eigenvalue Problem with Pseudospectral Chebyshev Polynomials
I am solving a linear 4th Order Eigenvalue ODE (Euler-Bernoulli Beam):
$$
{\frac{d^{4}w}{dx^{4}}} = - \alpha {\frac{d^{2}w}{dx^{2}}}
$$
The method I used was to apply a truncated spectral expansion ($...
0
votes
0
answers
56
views
What is the best finite volume method for the following equation?
I'm trying to create a partial differential equation that approximates 1-D climate in a rocky planet's atmosphere, which accounts for energy transport via radiation and convection. I am only ...
- 317