All Questions

I'm computing some phase transitions with KMC and having trouble with the magnitude of the time step, and possibly it's dimension. The idea is to compute the desorption of some molecules as a function ...

I'm trying to calculate the 2 perpendicular versors (unit vectors), $\vec{n_1}$ and $\vec{n_2}$, that define a plane whose normal versor (unit vector) is $\vec{n_n}$. For example, assuming that the ...

I am trying to calculate the best set of cuts for some wood cutting to reduce the waste. So: Given a set of numbers, the goal is to find the best matches below a limit (size of wood beam). Example of ...

Consider the potential given above: $$U(r) = \frac{U_0}{\exp[(r - r_0)/\epsilon] + 1}\, .$$ How to solve the Schrodinger equation with this potential numerically and find the eigenvalues?

I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity. Is there any outlet boundary types that avoids the reflection of flow from the outlet back ...

Question is mostly related to literature or suggestions. Given a semi infinite domain: $x=[0; +\infty);y=[0; +\infty)$. Willing to transform it to computational domain of: $[0,1]\times[0,1]$. I did ...

Suppose I have a square matrix $\mathbf{A} \in \mathbb{R}^{n\times n}$ and a vector $\mathbf{b}\in\mathbb{R}^n$. In my application I need to accomplish two things. I need to find the solution of the ...

I'm new to topics about optimization. I am currently reading about Steepest Descent Method in Gradient Descent optimization. I saw this equation where we need to find a new iterate with an initial ...

I wish to solve a linear system $A x =b$ in which $A$ is dense but not too large, say no larger than $10\times10$. However, I am not interested in the full solution vector $x = [x_0, x_1, \dots]$, ...

I am writing a proof-of-concept implementation of Newton's method for minimizing the negative log-likelihood term in a logistic regression model. I'm comparing the performance of a native python ...

I am trying to better understand the FAS multigrid algorithm for Euler equation in FV discretization. The usage of the modified residual (the residual with forcing) inside the different cases: ...

Context I have an array of objects (or a list of dictionaries), sorted in order based on a property of each object, say, time. In JSON, it would look something ...

I am new to this forum and to computational science in general. I started to learn numerical liner algebra on my own and would like to code a GMRES solver in python (no preconditioner for the time ...

I met a problem when I use the construction method to return the String the Thymeleaf can't get the user's value in Html. ...

Given $A\in\mathbb{C}^{n\times n}$, I want to use LMI or SDP to find feasibility of $x>0$ in the following inequality: $$(I-A^*A)+x(\frac{A+A^*}{2})\prec0,$$ where $D\prec0$ means that $D$ is ...

Recently, the application of Graph Neural Networks (GNNs) has become more and more extensive, and it has in many fields without topology，such as NLP. In several experiments, I have not got the STOA by ...

I am solving numerically the ODE $\ddot x(t)=-c\dot x(t) -\sin(x(t))+F\cdot \cos(\omega t), \;\dot x(0)=x(0)=0$ for $t\in [0,20\pi]$ on an $N=2000$ dimensional grid. I am working on Python, and I ...

I am interested in the iterative solution (preferably Krylov-type solvers) of a problem Ax=b, with x, b ∈ ℂn x 1 and A ∈ ℂn x n. A is symmetric, invertible, and its real and imaginary parts are ...

I am running a sensitivity study on the model $y(t) = x(t - \tau)$ where $y(t)$ and $x(t)$ are 2 time signals and $\tau$ a time lag. Basically I want to study the sensitivity of $y$ to a change in $x$....

I'm curious about the general case, but for ease of explaining lets just take the case of a $P^2(\Omega)$ approximation. For simplicity, let's also just consider the reference element $(0,0), (0,1), (...

I am considering implementing the accelerated inverse power (AIP) method with Rayleigh quotient to speed up eigendecomposition of a real square symmetric matrix. Halton (1996) gives an example ...

I am implementing a finite difference method for a PDE with a Neumann boundary condition. I will simplify my question to a single dimension. Suppose I have a PDE $$\frac{\partial u}{\partial t} = \...

I am trying to simulate the spread of mold in a petri dish using a cellular automata based approach. Thanks to the answer in my other question Stochastic cellular automata - algorithm limited by 1 ...

First post. Hi everyone. I’m trying to develop an algorithm to later code that schedules appointments in a way such that the number of hours occupied by the appointments in a given day is maximized. ...

Suppose I want to minimize below objective function $\sum | g(x_i) \cdot I_{g(x_i)<0} |^2$ i.e, the latter penalty terms like $ |g(x_i)|^2 $ are only computed when $g(x_i)<0$. $|g(x_i)|^2$ are ...

When solving a PDE numerically by domain decomposition methods, what is the "optimal way" to split the domain? Are there any results stating that a particular partition of the domain yields &...

I have learned about the finite element method (FEM) as a method for solving boundary problems given by a PDE. The way I learned it is to approximate the solution by a linear combination of test ...

I am studying the numerical resolution of 2d advection-diffusion problems with finite element methods. $$\frac{\partial u}{\partial t} + \beta\cdot\nabla u = \nabla\cdot(\nabla u) \, .$$ It is said in ...

I'm working on this project where I have to simulate a gold nanoparticle impact in a gold plate, my script is: ...

I was solving the time independent Schrödinger equation using the shooting method for harmonic oscillator potential. This is the code that I wrote for that with the results (code is written in julia): ...

I am trying to implement Large eddy simulation for solving air flow simulation with large Reynolds number using Smagorinsky sub-grid stress model. I read that the filter size should be calculated ...

In any asymmetric encryption specifications, there is a step where we need to calculate data ^ public_key mod e to get ...

New to stackexchange, so hopefully I’m posting this in the right place. Please let me know if you think this is inappropriate. I have a solution in search of a problem that some of you could perhaps ...

I have a set of $n(n-1)/2$ numbers. I should put them in a descend order، then multiply every set by this related value: the first set has $ {(n-1) numbers} \times\ 1$; the next set has $ {(n-2) ...

I have a system of PDEs describing atmospheric chemistry and transport. I use finite-differences to make my system of PDEs into a system of ~10,000 ODEs. I then integrate the ODEs forward in time with ...

I am having trouble implementing a model from a publication. Huang, K-L.; Holsen, T.M.; Selman, J.R. Ind. Eng. Chem. Res. 2003, 42, 15, 3620–3625 scihub link: https://sci-hub.se/10.1021/ie030109q I ...

I am trying to compute the area of an 8-node rectangular serendipity finite element from the equation $$ \sum_{i= 1}^8 det \, J(\xi,\eta) \cdot W_i $$ based on Gaussian quadrature, where $$ J(\xi,\eta)...

This question is different from the last one as I have changed $d$. I want $d$ that gives different values for different $F_t$. Note the equation is extremely long because I want the best measure of ...

Let $M_n(\mathbb{R})$ denote the set of $n\times n$ matrices with real entries. I have an $n\times n$ matrix $X\in M_n(\mathbb{R})$, and I would like to implement the linear operator $[X, \cdot] : M_n(...

I'm studying from Guermond lecture notes available at https://www.math.tamu.edu/~guermond/M661_FALL_2019/chap12.pdf (see Lemma 12.8( Discrete trace inequality).) Consider the simple case $p=r$, i.e. ...

I have an optimization problem, which is to maximize the following integral over the unit sphere: $$ \max_B \int d\Omega \mathbf{f}^{\dagger}(\theta,\phi) (B^{\dagger} + B) \mathbf{f}(\theta,\phi) $$ ...

I would like to calculate the number of floating point operations (Flops) my code is performing in my machine. To do so, I would like to be sure I am counting the operations in the inner-most loop ...

I am trying to estimate parameters, 4 of them, by fitting a system of 3 ordinary differential equations. I am using a model published that was using 3 parameters and gave a good fit to the data, and I ...

I am trying to reproduce the results from the hp-VPINN paper (https://arxiv.org/pdf/2003.05385.pdf) on tensorflow (v1) for Poisson's equation, particularly the two-dimensional Poisson equation. In one ...

I tried to implement the 2d advection problem with a velocity field, that is not constant in space. My problem is, that the "mass" of my shifted density gets "eroded" or just ...

Suppose we have a countably infinite $A$ and $F_1,F_2,\cdot\cdot\cdot$ are an infinite sequence of finite sets (denoted $\left\{F_n\right\}_{n=1}^{\infty}$) such that $\bigcup\limits_{n=1}^{\infty}F_n=...

Context Let's say I am trying to model the spread of mold in a petri dish, using a stochastic cellular automata approach. The petri dish can be thought of as a grid of 1mm x 1mm squares, each called ...

As we all know, the Additive Schwarz approach can be used as either solver or preconditioner, however, my question is, what is the difference between the two? In other words, how to use AS as solver, ...

I am an amature in python, I wrote a simple code in jupyter. But it is giving an error. I want to plot a function: ...

I am using COMSOL to solve a mathematical model involving thermoelectric hydrodynamic (TEMHD) flow. I am running a very large parameter sweep and using the solutions obtained to make some plots. ...