# All Questions

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### How to compute Singular value decomposition of a large matrix with Python

Language: Python3 Problem: I have a matrix Q of shape [51200 rows x 51200 cols] stored in a binary file, each of the element in this matrix has a data type of complex64. To load the data into memory I ...
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### Why Is This Python Code Faster Than Fortran Wrapper with F2PY?

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 ...
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### Dealing with Extra Categories in Test Set

Suppose I have a data set which consists a dependent variable y and independent variables X. Suppose that there is a specific ...
39 views

### Solving for a single element of a solution of a linear system

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 $x = [x_0, x_1, \dots]$, ...
27 views

### Multigrid method: linear solver and modified residual

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: ...
71 views

### Stable iterative solver for complex symmetric linear systems

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 ...
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### Formulating this optimization problem

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 ...
208 views

### (Lack of) Availability of Finite-Difference library for simple 2D PDEs

I would like to solve two types of simple 2D problems, namely the stationary heat equation on an L shaped geometry like this: And also compute the magnetostactic field in an air gap of the following ...
1k views

### Generate random smooth 2D closed curves

I would like to know how can I generate a collection of random 2D closed smooth curves. I thought about generating a random 3D surface with random peaks, and then intersecting the Z=0 plane with it, ...
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### How is FEM used in structural engineering?

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 ...
70 views

### "Optimal" domain partitioning in domain decomposition algorithms

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 &...
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### How asymmetric encryption is done very fast [closed]

In any asymmetric encryption specifications, there is a step where we need to calculate data ^ public_key mod e to get ...
6k views

### How does one determine the point group of a molecule?

You've managed to finally find out how the atoms are spatially arranged on your newly-discovered molecular entity. Through, say, spectroscopic means, you are now in possession of a bunch of atom ...
676 views

### Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3

I have a problem getting a sensible result for the Mean Square Displacement (MSD) for a simulation of $N$ particles under Brownian dynamics with Lennard-Jones interaction between them with or without ...
153 views

### How to include negative number in the log-sum-exp?

I want to know summation of some small numbers, such as {e^-1000, -e^1001, e^1002...} If all numbers are positive, I can use log-sum-exp algorithm. But unfortunately, negative numbers are also ...
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### How can i fix this error in lammps? [migrated]

I'm working on this project where I have to simulate a gold nanoparticle impact in a gold plate, my script is: ...
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### 2d advection-diffusion: cell Péclet number and numerical stability

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 ...
70 views

### Filter size of large eddy simulation with Smagorinsky sub-grid stress model

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 ...
90 views

### Question about step in the proof of standard discrete trace inequality

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. ...
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### Weird behavior in for solving TISE in harmonic oscillator potential using the shooting method

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): ...