All Questions

I am solving two different ODE whose solutions need to be matched. I am currently doing this by hand, which works great, but I would like to automatise this process. The second ODE takes one of its ...

I would like to enquire about a situation I encountered while using the scipy function scipy.optimize.minimize(method="SLSQP"). It seems to loose track of the global minimum in the path of ...

I am a first-time user of TIMESAT, and am attempting to follow along with this tutorial. http://rstudio-pubs-static.s3.amazonaws.com/452032_a5df2d3f782444fc830d43548a304ec5.html#PartA However, I am ...

I have a background in Computational Mechanics but my knowledge remains very user-oriented. What I mean by that is that I have a fairely good knowledge about how to use a commercial engineering ...

Related to: What are the negatives of using higher order finite diference schemes? Problem: I have some discrete data of a trajectory $x_t$ with errors $\delta x_t$ of a physical system sampled at ...

According to data processing inequality, no data processing technique, neither deterministic nor stochastic, can add new information to the original input. Many experiments, however, show improvements ...

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For studying a spin model on a lattice, I have to generate a random unit vector starting from a pre-exstisting one. There are multiple ways to do it, but the book I use suggests generating a random ...

In large sparse inverse problems, there are two terms that I don’t have a clear perception of them; Weighting and damping. I know damping relates to the regularization process and weighting is a ...

I have the following ODE - $\frac{dn}{dt} = \frac{1-n}{A} - \frac{u(t)}{B}n , -30\leq t\leq30, n(-30)=1$ where $A,B$ are constants and $n = n(t)$. I can solve this ODE analytically and get an ...

I have to convert some Matlab code into C++ code. These functions are used in this code. createOptimProblem(....) MultiStart(....) run() I have only basic ...

I am in the process if computing the Dual-Weighted Residual (DWR) for a linear PDE with a linear functional but I am struggling with the residual part of the calculation. For example suppose we want ...

I am trying to use Newton's method to get a stationary solution for a system of equations of the following form: $$ \begin{Bmatrix} \frac{\partial x}{\partial t} \\ 0 \end{Bmatrix} = \begin{Bmatrix} f(...

For the past weeks I have been trying to reproduce Agarwala's results but I've been unsuccessful. From this paper I am trying to reproduce the first and last columns of Fig.2, by implementing eq.2; ...

Consider the elastic equation $$- \operatorname{div}(C \nabla \mathbf{u}) = \mathbf{f}$$ as presented in step-8. Here $\mathbf{u}$ is the displacement vector, let's consider the 2d case. As you can ...

My task is to Implement the derivative with the 2nd order finite difference for 2D functions. Evaluate the accuracy of the numerical derivatives of J(x,y) at the point (x = 5, y = −2) by determining ...

This was originally asked on Stackoverflow but instead of migrating it was suggested I repost here and delete that one. I've tried to clarify based on comments there. I'm new to MPI, but I am trying ...

Using Scipy, I would like to draw a random sample according to a certain probability density. The probability density function I consider is defined on the real line and depends on k parameters that I ...

I was reading the following paper: The time-rescaling theorem and its application to neural spike train data analysis and I have some difficulties understanding the proof of the time-rescaling-theorem,...

I'm learning how to solve vector-valued problems with deal.II library. In particular, I'm looking at the following introduction from the official website https://www.dealii.org/current/doxygen/deal.II/...

I was trying to fit some data to a single degree exponential decay function but a*exp(-x*t) and a*exp(-x/t) gives completely ...

I am trying to understand the dyadic operation for a while since I am interested in Elasticity problems. I believe an intuitive understanding (rather than assuming) will give me good problem solving ...

I am interested in solving the equation $$ \begin{aligned} \nabla \cdot\left(\nabla \phi-\frac{\nabla \phi}{|\nabla \phi|}\right) &=0 & & \text { in } \Omega \\ \phi &=0 & & \...

I’m trying to implement the method of Balanced and Rebalanced Splitting in the following problem which is enclosed in Speth’s and Macknamara’s paper ‘’BALANCED SPLITTING AND REBALANCED SPLITTING’’. ...

I have just created a code snippet in Octave/Matlab that aims to create a plot which shows the accuracy of an initial probability vector $\vec{\pi}$ derived from the transition probability matrix $\...

I am working on a program currently that works out the maximum flow through a network using the Ford-Fulkerson algorithm, and that works fine, however, I need the final flow to meet the constraint ...

I'm writing a paper where I am discussing different types of construction heuristics. One type does not change previous decisions when adding new elements to the solution. I'd call them "...

While looking at step6 of deal.ii tutorials, I decided to try to understand how the constraints coming from hanging nodes are imposed. So I started by watching video lecture 16 by prof. Bangerth As ...

Given a large sparse (square) matrix in MATLAB, how can I extract the banded or the block-diagonal parts (of fixed size) of it efficiently? These are useful operations when prototyping and testing ...

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 trying to perform a two-dimensional random walk for a particle, but I am not getting the desired result. The plot produced is a linear plot, which obviously should not have been. Similar code for ...

Given numbers $x, y \in \mathbb{R}$ where $$\frac{|y-x|}{|x|}$$ is small, and code that implements the function $f$ with a sequence of arithmetic operations, I would like to compute to high accuracy ...

Apologies if this is a bit of a soft, unclear, or opinion-based question. I'm a relatively new PhD student in a (computational) quantum chemistry group. My group develops and maintains a few software ...

This question is related to the following: https://math.stackexchange.com/q/4151405/685910 - the context is summarized below for clarity. In the setting of convex optimization, I am looking for a ...

I am currently attempting to use FEnICS to solve an electrostatic problem with two materials of different permittivity $\varepsilon_1$ and $\varepsilon_2$ forming an interface: Consider a domain $\...

I am working on a combined contact, bending, and torsion problem. I have data on geometrical points and their instantaneous stress components. However, based on the available data, I have to ...

I am struggling to understand how scipy.solve_ivp() handles errors in a system of ODE. I have a complex systems of ODE with very large varying time-scales, for which my state "y" is composed ...

I am interested in solving the transient advection equation $\left\{\begin{array}{ll}\partial_{t} u+\beta \cdot \nabla u=f & \text { in } \Omega, t>0 \\ u=0 & \text { on } \partial \Omega^{-...

I am create syntetic data from a system of differential equations describing the COVID-19 epidemic and then I try to use the method SINDy to recreate the differential equations from the data. Link to ...

I have two vectors $r$ and $m$. Both vectors are $N\times1$. A function is calculated as - $F(1:N) = \phi r + (r^3 + rm^2)$ $F(N+1:2N) = \phi m + (m^3+mr^2)$ ...

I am new to GNU Octave 6.2.0 on Linux, and I am trying to use the package 'parallel' to make use of 24 threads on my machine. I have an array (array1) that has ...

I am currently learning nodal DG methods, primarily through the book by Warburton, and am a bit confused on how to handle surface integrals using straight edged elements. On page 187 (and on page 214)...

I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ...

Customer satisfaction is generally an ordinal variable on a scale of 1 - 5, where 5 is the best score. Ordinal regression is used to regress such variables. Can Catboost Regressor, handle such a ...

I will now explain what I understand to be the process of a finite element mass matrix assembly. I would like a reference which does something similar, or if I am mistaken about the process please let ...

I'm trying to do a simple implementation to study the advection-diffusion-reaction dynamics in a straight pipe. I have points positioned along the length of the pipe (blue dots in the image above). I ...

I have the equation $F(t) = \phi u + \frac{1}{2}\frac{d^2u}{dt^2} + u^3$ and broadly speaking, my task is to calculate the $\phi$ and $u(t)$ such that $F(t) = 0$. I am testing out a new algorithm to ...

I am building a quantum circuit simulator using mpi4py. The simulator takes user inputs to build the initial system and quantum gates the system passes through. I can get the code to work if I do not ...

I would like to ask a question on the stability of BDF2 applied to hyperbolic PDEs. Say I have a hyperbolic equation as $\frac{\partial c}{\partial t} + {\bf U} \cdot {\bf \nabla}c=0$. This system is ...

I have a complex Hermitian matrix of size about $70000\times 70000$. I want about 100 eigenvalues near 0. However, I know that every eigenvalues are two-fold degenerate. I found out that the running ...