All Questions

I am solving the heat equation using a 1d finite element method with backwards Euler time discretization. What happens when the time step is greater than or equal to the spatial step and why? Edit - ...

I am doing a code that can calculate the hartree-fock energy. I want to form the two-electrons integral array by reading the data from the input like this one below to calculate the Fock matrix. Note:-...

I'm having trouble with the following implementation of the KS model (see below) found on Solving numerically the 1D Kuramoto-Sivashinsky Equation using spectral methods When tN > 300 an overflow ...

I have been trying to solve this equation and write the finite difference scheme in matlab for months, but I still am not successful. Given the KdV Equation $$\tag{1}u_{t} -6uu_x+u_{xxx}=0$$ I have ...

I'm new bee in computational physics. I know theoretically what is probability distribution mean, but I'm little confused how to implement this theoretical concept. SO for example we've trajectories ...

I am trying to numerically evaluate the following Duhamel's integration: $$ x = \frac{-1}{\omega_d} \int_0^t \ddot{x}_g (\tau) e^{-\zeta \omega_n(t - \tau)} \sin{\left( \omega_d (t - \tau) \right)} d\...

I have a euqation: P(a) = a^(-b)+C. I have 15 randomly generated 'b' values in a list list_x....

I simulated Oja's rule and BCM for a single postsynaptic neuron with two presynaptic neurons, and for 10000 inputs, where I randomly select one of $(0,1)$ or $(1/2,\sqrt{3}/2)$ as input. My learning ...

I have a set of points $P$ and want to find the ellipse with the smallest area that covers at least a fraction $f$ of these points. How can I do this? These questions ask the same thing, but folks ...

I would like to write a simple finite element solver in python in order to solve 2D Poisson equation and then visualize it. $$ -\nabla^{2} u(x,y)=f(x,y), \quad x,y \quad in \quad \Omega\\ u(x,y) = u_D ...

My current work requires using (Adaptive Mesh Refinement) AMR to resolve multi scale physics. I have a general question whether finite element is better than finite difference in this aspect or not. I ...

I have a layer of atoms on a surface and am trying to do a 2D Frenkel–Kontorova-like energy minimization using at first simplex then once that works, with simulated annealing. The number of atoms ...

I have a system of PDEs constituting an initial value problem (IVP) consisting of three coupled PDEs: \begin{align} \partial_t \rho + \partial_x(\rho v) &= \left(k_A (1-\phi) + k_B \phi \right)...

I would like to ask a question on the implementation of finite volume method on a non-uniform grid in solving Navier-Stokeq equations. I will just post the screenshot of a PhD thesis, where I found ...

I am using Immersed Boundary Method to simulate elastic particles in 3D Stokes flow. Specifically, one has $\nabla ^2 \mathbf{u}-\nabla p + \mathbf{f}(t) = 0$, $\nabla \cdot \mathbf{u} \; $, where $\...

I am trying to find the peaks. I have list x_period and y_power. I find the peaks from the ...

It was suggested on math.stackexchange.com that I try to ask this question here. Consider a bounded linear operator $A : U \to V$ where $U$ is finite dimensional and where $V$ is a separable Hilbert ...

I have a problem which I believe is numerical instability when trying to solve a heat conduction equation using finite difference. The short version is that when the parameter $I=80.3$ I get the blue ...

I'm new to VMD and I'm having some problems with displaying my polymer chain. Instead of just one bond, VMD draws multiple bonds. Why does this happen?

Suppose we have a linear algebra problem with a banded matrix A which has nonzero entries on the main diagonal, two nearest sub-diagonals, and two other sub-diagonals (such band structure often arises ...

Let $A\in \mathbb{R}^{n\times n}$ and $v \in \mathbb{R}^n$. We recognize $Av=\lambda v$ for some scalar $\lambda$ as an eigendecomposition problem. Suppose $\mu \in \mathbb{R}^n$, and let $\odot$ ...

I am trying to simulate solute transport of acid (HCl) and consequent mineral dissolution around a grain (calcite). The governing equation for transport is the advection-diffusion equation, given as: ...

Given n sets of points in general position in dimension 2 (n typically small, 2-6), can one find tuples of points, one from each of the sets, which are close in some sense (the closest, mutual ...

Consider an optimization problem of the form: $$\max_{f(x)\le K,\\0\le x\le M} c^\top x,$$ where $f(x)$ is nonlinear. Can a line search of the following form be used to solve this problem? $$ \max_{\...

How to position oneself, if one has little practical engineering background or function, but may have a broader insight into mathematical modeling? Or, lets say: I could write models to prove ...

Naive restriction operators in geometric multigrid that I have seen are typically implemented as a convolution and a subsequent averaging of every two entries in a vector $v^h$. For example: $$\tilde{...

I found in A Multigrid Tutorial: Second Edition by William L. Briggs‏, Van Emden Henson‏, Steve F. (here) the following Schemes: Two-Grid Correction Scheme, p. 37: And V-Cycle Scheme, p. 40 I want ...

Suppose I wish to solve a linear system $AX=B$ iteratively where $A$ is an $m\times m$ matrix and $X,B$ are $m \times s $ matrices (not single vectors). Instead of solving $s$ independent systems I'm ...

For IEEE, the single representation is 1-bit sign, 8-bit exponent and 23-bit mantissa. This means that at each exponent value, you can test all 2^23-1 (roughly 9mil cases) possible combination of ...

in our finite element class we were talking about interface problems our teacher came up with the following, where $K_i$ are two given functions and $u_i$ is the restriction of the solution $u$ to $\...

I need to evaluate the hypergeometric function $_2F_1$ with $|z| > 1$ as in Wolfram Language with GSL but the GSL documentation says the $_2F_1$ needs $|z| < 1$. Is there any way I can use GSL ...

The "standard" box-stacking algorithm(s) AFAIK assume a single stack and try to put the "largest" boxes on the bottom. The case I want to solve is simply to distribute the N boxes ...

Computer make it possible to find information in large databases. However, the results are often too large to be returned in their entirety to the user who requests them. Computer therefore sort the ...

I'm trying to estimate DOA in the Hybrid architecture using root music so I need to solve the attached equation to find the roots for the Root_Music equation in Matlab. Does anyone have an idea for ...

So I recently encountered this question in my head while taking my Scientific Computing class, where the lecturer talked about computing numerical error of a scheme. My guess would be that we take a ...

I know that NumPy has linalg.cond(A) to find the condition number of a matrix A. But, if I want to find the condition numbers of the roots of a large polynomial ...

In Maple, I have a function $f(x(t),y(t),t)$ that I want to differentiate with respect to $t$. I know the command for partial derivative $\frac{\partial f}{\partial x}$,$\frac{\partial f}{\partial y}$,...

Without dwelling on details on how to obtain the HJB equation for this problem, I would like to know if the scheme I wrote for solving it numerically is viable or did I miss something. I need to solve ...

We can use the $RT0$ to solve the Darcy equation, i.e. $$k^{-1}\mathbf{u}+\nabla p = 0, \text{ in } \Omega,$$ $$-\nabla \cdot \mathbf{u} = 0, \text{ in } \Omega,$$ $$p = p_D \text{ on } \partial\Omega,...

I know the Lie symmetry group of the harmonic oscillator differential equation from the literature. It is an 8 parameter Lie group. 5 of these generators generate Noether symmetry: $$G_1=\sin(2t)\frac{...

I implemented Node-To-Surface contact algorithm (Wriggers, Peter, Computational contact mechanics., Berlin: Springer (ISBN 3-540-32608-1/hbk). xii, 518 p. (2006). ZBL1104.74002.). The code is done by ...

I have to give a presentation on unsupervised learning in 2 days, and I have to explain/show the equivalence between Hebb's learning rule (or Oja's rule to be more specific) and PCA. The thing is that ...

The test functions of general finite elements are like interpolation functions (if my understanding is correct). But how about test functions of Raviart-Thomas elements? Let's raise the $RT0$ element ...

The aim is to solve the below equations and plot $m$ with time, i.e. $\frac{dm}{dt}$ $k$ is unknown and needs to be estimated. For the parameter estimation, the below values in the table for m versus ...

I am trying to simulate the following equation using FDTD $ \left(- \partial^2_t + \partial^2_x + V(x) \right) \psi(x,t) =0 $ subjected to the initial conditions $\psi(x,0) = f(x),~ \partial_t \psi(x,...

I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...

I have the wave equation $$u_{tt} = 4 u_{xx}$$ with the boundary conditions $$u(0,t) = u(L,t) = 0\,,\quad x \leq 0 \leq 2\pi \,,\quad t\geq 0$$ and initial conditions $$\begin{align} &u(x,0)=\...

I have a linear system $Ax=b$ resulting from a finite element discretization of the Poisson equation. I am applying an IC0 (incomplete Cholesky ($LDL^T$) with the same sparsity as the original matrix) ...

I have the following code ...

I found out the conserved current for harmonic oscillator with angular frequency 1, particle falling in gravity close to ground ($g=1$) using maple. I'm unable to understand the result: $$J[t](t, x(t)...