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I have a function $f(x)$ defined on a domain $D$, but such that the image $f(D)$ may contain extra regions not included in its domain. I am interested in solving the fixed-point equation $x=f(x)$. If ...

I am trying to perform the following integral $$\iint_V \frac{r'\left(e^{-r'^2/2\sigma^2}\right)\left(r-r'\cos(\theta-\theta')\right)}{r^2+r'^2-2rr'\cos(\theta-\theta')}dr'dθ'$$ Using Gauss-Hermite ...

1 I am wanting to import an Excel file into panda's, in the below format. From my novice eye, it seems to be returning an XML file. Is this correct and could anyone point me towards how I get this ...

I have a function $f:\mathbb R^N\to \mathbb R$ and I would like to compute all the partial derivatives of $f$ w.r.t. the $N$ input. What is the computational complexity using the (ones-sided) finite ...

I'm trying to plot the cross section with respect to the photon energy $h\nu$ but for $\gamma = 1.0, 1.2, 2.0 $ in the same axes $\sigma = \left[\left(\frac{\xi_{eff}}{\xi_{0}}\right)^2 \frac{n_r}{\...

I am really new in Python and I hope this is the right community for my question. Sorry if it is not. I am trying to import data from a .txt file with pandas. The file looks like this: ...

Let $D$ be a sparse matrix. I want to compute $D\times D^T$. As $D$ is fairly large, so I am row-slicing $D$. That means for a range $(i,j)$, I am computing $C = D(i:j,:) \times D^T$ and performing ...

Recently i am studying about the 1D EM-PIC simulation (EM-PIC = electromagnetics plus particle-in-cell, simultaneous time-integration of the electric/magnetic fields plus the motion of free charges ...

Can anyone help me to explain the phasor form of Maxwell equation in MATLAB along with the MATLAB code .I will be very thankful to you .

I'm creating a FEM simulation based off of the Thermal Diffusion Equation: https://en.wikipedia.org/wiki/Heat_equation I allow users to select and set the initial temperature of elements (cells) ...

I have the following dynamical system, $\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$ $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \label{2}$ $\eqref{1}$ represents the exact ...

I wasn't sure if this is a Computational Science SE question or a Stack Overflow question but I think it's more of this one. I wanted to make a graph where I can rotate a hyperbola (not parabola or ...

I have an integral of a convolution between two functions. How can I calculate this in Python? It is a continuum convolution.

For a scalar quantity $u = u(x, t)$, I'm considering the transport equation \begin{align} u_t + au_x &= 0, \qquad{x\in[0, L], \ t\in[0, T]} \\ u(0, t) &= u_{\text{in}}, \\ u(x, 0) &= f(x). ...

In the BFGS method we perform iterations by calculating an approximation $\boldsymbol{H}_k$ to the inverse Hessian $\boldsymbol{H}$ of the objective function. This method belongs to a family of ...

I am working on an Inverse Scattering problem in microwave imaging. I went through the book -'Introduction to Imaging from Scattered fields' by Michael Fiddy et. al. They have used COMSOL for the data ...

I'm a master's student in Math interested in Numerical Analysis. I know there are lots of questions like that on this site, but I think this is the best place to ask. So, I'm looking for an ...

In the one to many assignment problem, many agents can be assigned to a task. In my problem, I want to assign many agents to a task, but for all of the agents assigned to that task, they must share a ...

For sure, there has been many highly optimized library on this. But I am working on a matrix-free context since the problem size does not allow explicit storage of sparse matrix elements. I'd love ...

We have a 3-dimensional grid of voxels (or cells), with individual voxels being of volume $dx\,dy\,dz$ where $dx=dy=dz=1$. A cone-like surface is defined by some function, $z = f(x, y)$, which in ...

I recently read the paper "On Spectral Clustering: Analysis and an Algorithm" by Ng et al. Much of the paper centers on Theorem 2 and equation 8. To me, it appears there is no given or referenced ...

I doing very intensive calculation with GNU octave. I plan to write other codes more laborious, so I need a language optimized for numerical computation. Because of performance, I think that a ...

I've successfully implemented a 1D DG code with non-normalized Legendre basis and I've now moved onto developing a 2D code using tensor products. For my 2D code I've chosen to have normalized ...

I have been learning petsc recently and made a simple solver for stokes equation on 3D staggered grid. My code is running on server with 200GB ram, but if I run a solver on 256^3 grid, memory used by ...

The classical Clenshaw recurrence (see Algorithm 3.1 here) is less accurate as $x\to \pm 1$. So Reich proposed a modification to it, which is discussed as Algorithm 3.2 as well as by Oliver. While ...

I have the following dynamical system, Equation 1: $\frac{d \phi}{dt} = -M^TDM\phi$ Equation 2: $\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi$ Equation 1 represents the exact dynamics of a ...

DISCLAIMER: PLEASE DO NOT PUNISH ME FOR THE .JPGs I) The Problem There's a particular metric $[1],[2]$ in general relativity which is written as: $$ds^{2} = -[c^2-v_{s}^2f(r_{s})^2]dt^2+v_{s}f(r_{s}...

I have a bunch of .json files, say 1000. To read each files I run the following code in MATLAB fname = 'C:\Users...\d90f3c62681e.json'; val = jsondecode(fileread(fname)); the output is as follows. <...

I am trying to solve an ODE with solve_ivp, but I am getting strange errors. Documentation: https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html ...

I'm trying to solve the following equation with FVM $$u_t + f(u)_x = g(u)$$ where $g$ is some smooth function of $u$ and $f(u) = \frac{u^2}{2}$. This is really similar to Burger's equation, except ...

I am using the XMDS library for solving the stochastic (projected) Gross-Pitaevskii equation $$i \hbar \partial \Phi\left(\mathbf{r},t\right)_t=\hat{\mathcal{P}}\left\{(1-i \gamma)\left(\hat{H}_{\...

I am doing a molecular dynamics simulation of Leonard Jones 6-12 potential. But instead of converging to a particular value. It always stays between -5.58 to -5.62. The standard value is -5.517. The ...

How long should the hyperelastic equations be solved before updating the mesh? To be specific, I'm interested in the hyperelastic model with a neo-Hookean solid: $$ \nabla\cdot\sigma + f = \rho\ddot{...

Between the two ears in the following bunny images, there are some degenerate triangles I want to detect. It looks like a volume-less thin slits. If the question is not clear, please let me know.

I tried to generate 3 very simple cylinders, each other connected to it end, however the cylinder get connected to an unexistent point in space as the image shows: It was supposed to each segment be ...

I'm looking for an open-source library for the generation of random n-dimensional orthogonal matrices in C++. In python, it looks like such a function is available in the NumPy package. But I was not ...

I've encountered a program where np.tensordot was used, so I tried looking it up but I can't really understand what this function is doing... I feel rather ...

I'm looking to learn C++ primarily from a scientific computation perspective. The approach of the textbook seems ideal to me as it covers C++ from first principles with an emphasis on numerical ...

I have two sparse general matrices stored in CSR format I need to multiply. Is there any chance to gain performance using AVX2? In general the matrices are big (hundreds of millions of non-zeros and ...

I am solving an optimal control problem of the form $$ \min_u \qquad\int_0^T \langle u(t), u(t) \rangle \, \mathrm{d}t \\ s.t. \quad \dot{x} = \tilde{f}(x) + u, \quad x(0)=x_0 \\ \qquad \tilde{\Phi}(...

A decade ago I saw a ~20 coupled state + random number problem that was used as a benchmark for meteorological CFD tools. It had a fractal dimension (of the chaotic attractor) around 2.3, I think. I ...

Let's say I have a set of data (1-D array) called charge density along the $z$ direction (obtained from DFT calculation), and I want to integrate it twice with respect to $z$ coordinates points (i.e., ...

I recently asked a question about this topic, but too much was unclear to me at the time which yielded poor response. (You can find the previous question here). Anyway, I am now trying to solve the ...

I am trying to implement the algorithm in this article. I have already asked a question before about it here, and I am trying to figure out what I am doing wrong. This time, it's this section of the ...

Suppose there are two arrays (They have the same length), I want to give a quantitative description about the similarity between them. I define a formula like this, which means we can shuffle them ...

Suppose to calculate the continued fraction expansion of $\pi$, the common-sense algorithm would be to take the decimal part, perform inversion, which will give the next term as integer part, and the ...

I'm recently studying for the spectral solver to implement EM-PIC code. I read an article and have some questions. Many PIC codes uses spectral solver to overcome numerical artifacts on FDTD. In the ...

Suppose I have a long, possibly infinite, sequence $x := [x_1, x_2, ...]$, and I want to use it to compute another sequence $y:=[y_1, y_2, ...]$ where each element is the sum of the last K elements of ...

I am using LeVeque's book: https://faculty.washington.edu/rjl/fdmbook/ Suppose I want to compute $u''$ using FDM with $\alpha=\beta=2$ (centered) so the FDM is $$ u''=\sum_{m = - \alpha}^\beta a_mu(...

I want to estimated the parameters $\ \hat{\theta} $ of a model using an iterative search for the minimum of a cost function. The cost function is defined as follows: $$ V_N(\hat{\theta}) = \frac{1}{...