All Questions

I am facing the following problem, formulated in practical terms: I have a region $\Omega$ in two or three dimensions, represented as a binary mask, and an initial density $u_0$ within that region ...

I have a first order system which is described by the following differential equation: $\ \dot{x} = -a*x + b*u $ where u is the input $\ u = 5*sin(3*t) $ and also the state ...

Based on this, pp 245, we go through these steps to discretize a gradient statement, namely $\nabla\phi$: 1- Gauss theorem reads, $$ \int_V\nabla \phi dV = \oint_{\partial V}\phi dS $$ 2- Integral ...

I want to calculate the stray magnetic field from a ferromagnet using the scalar potential method (1). The problem consists of a ferromagnetic cuboid divided into small cuboidal cells in which the ...

I am aiming at keeping my scientific studies and analyses reproducible: I am automating them as much as possible, I am sharing them, and I sharing them together with the execution environment(s) I've ...

I have a first order system which is described by the following differential equation: dx/dt = -a*x + b*u where u is the input <...

What I wanna solve it the problem following ( by quadrature method ) I want to get two arrays of data ( z & tau ) from z[0], tau[0] to z[2249], tau[2249]. Since the integrand diverges at z=0.9, ...

I am new to METIS and trying to use it in my fortran code. I read the manual online. But still, I am not sure about how to implement it my code. I tried the test cases in the graphs directory. For ...

I have some discrete data, non-equispaced in x, y=f(x). I want to use a numerical finite difference method to calculate the second derivatives of y, at some point. I am using the Fornberg method, ...

Hello fellows and folks. I have been looking to do this for 1 month and still cannot find the way to do it. Here’s what’s going on: I have a csv file called ratings.csv with the following ...

Consider a system of PDEs $$ \begin{cases} u_t = \nabla \cdot (D(u)\nabla u) + \frac{c}{K_U+c}u-ku\\ c_t = d_c\Delta c -\frac{\nu_U c}{K_U + c}u \end{cases} $$ with some boundary conditions. Here, $D(...

Are there well-established approaches to single-variable multimodal optimization? Given $f:\mathbb{R}\rightarrow\mathbb{R}$ that: has several local minima within a given range of interest $[a,b]$ is ...

I am trying to study the stability of numerical discretization schemes using the Jacobian matrix of the residues with respect to the vector of conserved variables. For a simple diffusion equation ...

In DFT, forces are calculated using the Hellman-Feynman theorem, such that: $$\frac{\text{d} E_\lambda}{\text{d} \lambda} = \left \langle \psi_\lambda \left|\frac{\text{d} \hat{H_\lambda}}{\text{d}\...

I'm using Nevergrad by Facebook in Python and am observing some strange behaviour relating to bounds. Let's find the minimum of a standard simple function: ...

After long hours of searching for an answer I thought it might be better to ask the community. The problem I have is that I need to convert STL files to mesh files. I know that I therefore need to ...

I have built an ANN model with 5 hidden layers and 100 nodes in each layer to solve a multilabel classification problem. After the first run, I get a training accuracy of ~66% and a test set accuracy ...

I'm describing some work on my website, and I'm wondering if my math modeling and computer simulation work is described ok: I say math modeling and numerical simulation. Should I say "...

I need to solve capacitated asymmetrical vehicle routing problem with time windows on ~30k points. Time limits for calculations are 2 hours. I've tried using Clarke and Wright savings algorithm, it is ...

I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows: When a certain problem is ...

I want to know the time complexity of following code Say I have a list unique_element[] There is an array which contain elements {4,5,2,4,7,8,1,5,9,8,1} Now as per my code I want to find out the ...

This question is originally posted in Quant.StackExchange but has been unanswered for some time so I ask in here. To make this simple let us consider the Geometric Brownian Motions (GBM). My ...

EDIT: I am trying to specify my Question. Also I am not going to clearify which spaces I use, because I am only interested in the basic idea. I am looking at a standard elliptic second order PDE: \...

I have the following, functional, XMDF file (version 2, or something like that) which I use to describe HDF5-stored heavy data for visualization in Paraview. I would like to upgrade to XDMF3 (just to ...

Based on the Navier-Stokes equations and a few parameterizations, the horizontal steady-state wind $u(z)$ within a forest of height H satisfies: $$ a\left(\frac{du}{dz}\right)^2 + b\frac{du}{dz} \...

I'm a beginner user of FEniCS and still struggling with some of the basics. Specifically, I have some issues doing the tutorials in the Langtangen-Logg book Solving PDEs in Python - The FEniCS ...

I'm trying to find the capacitance matrix for a small array of metal boxes in air using Comsol 5.4. The geometry presented here is a simple geometry that recreates the problem I'm experiencing. ...

I use OpenFoam 5.0. I Want to print or save in xlsx file the matrix A and B in equation Ax=B in OpenFoam Solvers. Can anyone guide me?

I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways. One of these claims is that my proposed solution requires no explicit SVD and ...

Background： I have an equation which looks like as follows: $W \times P = R$ $$\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \...

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...

I'm creating too much throw away code for interfacing with the scipy optimize package in a user friendly way. (See code below for example of interruptible optimization that keeps last optimization ...

Please consider the assignment I have uploaded on the picture. I am confused about the functions $g_L(t)$, $g_R(t)$ and $\eta(x)$. What are they and how do I find them... My question: Is it possbile ...

I have calculated the eigenvalues of Hamiltonian by exact diagonalization. Now I want to plot density of states (DOS) on y-axis and E on x-axis. DOS counts the number of energy levels in unit interval ...

I am trying to find the solution of linear advection equation of the form: $\frac {\partial c}{\partial t}+u\frac {\partial c}{\partial x}=0$ $c(x,0)=0$ $c(0,t)=\{c_0 \ \text{for}\ t \leq t_1 \text{...

Let's assume, that we have damped harmonic oscillation of a body in the form of a cone, immersed in a liquid. Equilibrium condition of the body is: $$m\overrightarrow{a} = \overrightarrow{F_\text{...

I would like to solve the following equations simultaneously and numerically for all $X, Y, Z, W$ where i = 1:Nw, j = 1:Nl, k = 1:K. $W_\text{net1}$, $W_\text{net2}...

I am trying to solve a non-convex optimization problem using fmincon(). At each iteration, I am iteratively looking for the optimum value and when the termination ...

I'm working on a gravitational n-body simulator and would like to implement dark energy into it but all I can find is papers with relativistic equations which I don't really understand. Is there a ...

I am trying to animate a plot of two distinct points (blue and green points) moving about the complex unit circle using Python's Matplotlib library. The problem I am having is that the animation does ...

I am using PETSc and libmesh to solve a simple linear elastic problem with quite complicated geometry, using linear tetrahedral elements. I am always using the KSP CG as the solver. I noticed that ...

I'm using BFGS to optimize a smooth but non-convex function $f$ that is computed by a simulation. The simulation also gives me a semi-analytical gradient $g$, which is verified by the numerical ...

Is the theory of 3d finite element method just an assembly of 2d finite element analysis by putting planes on top of each other, or, a much more comple and different theory applies for 3d, with ...

When gmsh uses higher-order tetrahedral elements, there is an underlying Lagrange basis used to specify the map from reference space to the element. I'm trying to load a gmsh mesh of 3rd degree ...

I have a matrix $A\in\{0,1\}^{d\times n}$ and $rank(A)=d,d<n$, and another matrix $X\in \mathbb{R}^{d\times n}$, but I do not know the rank of $X$. What can we say about the rank of their Hadamard ...

$[\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}]u(x,y)-6[\sin^2(x)+\sin^2(y)]u(x,y)+4.1209 u(x,y)=0$ with the periodic boundary condition $-4\pi <=x,y<=4\pi$. How to write the ...

In Higham's Accuracy and Stability of Numerical Algorithms, Chapter 15, algorithm 15.3 and 15.4: The topic is ostensibly condition number estimation, but these algorithms show how to compute $\gamma$ ...

I have implemented the Gillespie algorithm on a 2D lattice where at each time step a randomly selected reaction can occur. Either: A node randomly moves (movement); Two neighboring nodes interact to ...

Hoping I'm not misunderstanding the concept here, but it is my understanding that Voronoi Diagrams and Delaunay Tesselations are 'dual' to one another, owing to the fact that each' solution makes ...

I have this non-linear partial differential equation. $$ \frac{\partial C}{\partial t}=\left(\frac{\partial C}{\partial x}\right)^2+C\frac{\partial^2 C}{\partial x^2} $$ I want to use the finite ...