All Questions

The function $\coth(x) - 1/x$ has a removable singularity at 0. Its Taylor series is: $$ \coth(x) - 1/x = \frac{x}{3} - \frac{x^3}{45} + \frac{2x^5}{945} + \ldots $$ I would like to evaluate the ...

I am developing a practical work of the following system of ode \begin{align}x'(t) &= k_1h(t) - (k_2+k_3)x(t)\\ y'(t) &= k_3x(t)\end{align} and $z(t) = (1-k_4)(x(t)+y(t))+k_4h(t)$, where $h(...

For my current work, I need to remesh a given geometry with Gmsh (currently trying all Gmsh versions to achieve this) to continue my Abaqus simulations. As can be seen in the image, the geometry has ...

I'm doing an experiment on synthetic data and I want to generate enough data but not too much. So I wonder if there is any rule for the minimum number of projection angles and detector count. For ...

I am trying to determine quality of my mesh elements using the Jacobian determinant as the measure. My algorithm takes vertices of nodes in triangular mesh and moves them around so as to form ...

I am looking for packing spheres (can be monodisperse or polydisperse with known radii distribtuions) inside a geometry. I am sure this is a well explored scientific problem with applications in ...

I have a really big symmetric 7.000.000 X 7.000.000 matrix that i would like to invert. The matrix is extremely sparse and it can be rearranged as to become a block diagonal matrix. The biggest blocks ...

Given two strings, PRINT (YES or NO) whether the second string can be obtained from the first by deletion of none, one or more characters. Input Specification Input will contain two strings ...

I am using the Numerical Recipes version of the Bulirsch-Stoer method to integrate an ODE with adaptive time step ("Numerical Recipes", section 16.4): ...

I would like to optimise the heat transfer on a PCB. Several dies are on the top and cooling air is going through the fins in heat sink on the bottom. The assembly consists of several layers like ...

I need to evaluate a sum of values that are on many different orders of magnitude in scale but might be signed. I’ve had great luck with the “log-sum-exp” trick for an unsigned version of my problem, ...

Given a multistage stochastic program, its solution (if it exists) consists of the first decision vector, as well as all the recourse decision vectors for all possible scenarios of an event tree. But ...

I have a stable numerical solution for the equation shown below. However, using a simple separation of variables an instructor demonstrated non-existence of the solution for such problem. Could ...

A similar question was asked here and the given answer is perfect for a unidimensional integration. I need to make bidimensional integration in R with a Gauss-Hermite quadrature: $$\int_{R^2} h(p1,p2)...

I have a nonlinear solver for equation $g= c_1f(x_1,y_1)+c_2f(x_2,y_2)$. Note that $c_1$ is much bigger than $c_2$. So after using Levenberg–Marquardt algorithm, I could only get $x_1$, $y_1$ and $...

I'd like to know whether the Hagen-Poiseuille equation can be used to solve for the velocity of fluid when the Reynolds number (Re) is less than 1. From textbooks, I understand that the Hagen-...

Given a volume (say, some polyhedron), I need to fill it with smaller polyhedra, such that the space is filled as much as possible. The constraints and relaxations are: (0) For a computation ...

I want to solve the following sets of n coupled equations. Initial values of $x_{n}(t)$ and $p_{n}(t)$ are specified. The problem is, I have an 1D lattice where every particle is bound with ...

I was wondering about the last paragraph in Matrix Computations (4th edition) by Golub, Chapter 11 (11.3.3), specifically his explanation of subspace strategy for Conjugate Gradient. Note that in ...

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 ...

I am trying to simulate the propagation of a gaussian beam through a lens using an FFT approach. I tried to implement the approach described by Couairon in this paper at page 43: https://link....

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I am applying optim() function in R to obtain maximum likelihood estimates of the fixed effects and random effects in a model with bivariate random effects. The ...

If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$...

I have a TTree in ROOT with 1000 events and 15 variables associated to each of them. I would like to convert this in its entirety to an hdf5 dataset. How do I organise my data in HDF5 Groups such that ...

I want to simulate human erythrocytes in capillaries. I calculated, that for a 1 meter long and 1 mm in diameter capillary there are about 3 billion blood cells. Erythrocytes are actually discs, but ...

In the previous question "Motivation behind Galerkin method", Paul gives a good and easy-to-understand explanation indicating that the Galerkin method is a kind of projection method. Can anyone ...

For a project in my advanced numerical method class I have to solve the 1D Kuramoto-Sivashinsky equation. $$ u_t + u u_x + \lambda u_{xx} + \eta u_{xxxx} = 0. $$ As explained here I will solve it ...

A Fortran code that solves stiff PDE systems contains the following arrays of Rosenbrock-Wanner method coefficients: ...

For Generalized Minimal Residual method GMRES, we usually use the Modified Gram-Schmidt MGS to generate an orthonormal basis of ...

I have a delaunay triangulation for a 2d box with say an airfoil inside. If I uniformly refine this mesh by subdividing each triangle in the mesh into 4 triangles by halving each edge, is the ...

For Householder transformation, we know that $H = I-uu^T$, where $\|u\|_2=\sqrt{2}$. When it acts on any vector $x$, $Hx$ and $x$ is symmetric with respect to $span(u)^T$. But I have read a ...

The usual story of Givens rotations vs Householder reflections is that Householder reflections are better if you want to map a long vector to $e_1$, while Givens is better if you want to map a 2-...

Here is an implementation of the sign function in C++ using Adolc librairy for automatic differentiation. ...

I have a question about HSS preconditioner with GMRES method. For implementing the HSS preconditioner with GMRES, we need to solve the linear system of the form (I + H)(I + S)z =r, for a given r at ...

For a project in my advanced numerical method class I have to solve the 1D Kuramoto-Sivashinsky equation of which I know little. I just know that it was derived the equation to model the diffusive ...

What are some computationally efficient ways to solve matrix exponentials, i.e. functions of the form : f(X)=$e^{X}$, where X is a square matrix ? So far I have been able to diagonalise some ...

My system is a symmetric FE problem with lagrange multipliers: $Z=\begin{pmatrix}A & C^T \\ C & 0\end{pmatrix}$ The matrix $A$ is positive semi-definite, non-invertible. The whole matrix is ...

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...

I'm trying to compute efficiently the following \begin{equation} A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k} \end{equation} for $j = 0,1, \ldots, K-2,K-...

In quantum mechanics, the wavefunction of N electrons is given by a determinant. I am working on a Monte Carlo algorithm. At each Monte Carlo step, I need to add or remove an electron, which means ...

Given a rectangular Toeplitz Matrix $ H $, how could one solve: $$ y = H x $$ For instance, $ H $ can be Linear Convolution Matrix of the filter $ h $: $$ H = \begin{bmatrix} {h}_{1} & 0 & ...

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...

I am beginner in MATLAB and similar. I sow and discussed with my professors doing simulations some times: they wrote down a lot of calculus, most of them using Crank-Nicolson Method and so implement ...

I am using the Armadillo library to solve a 3d heat conduction problem on 3d unstructured grid system,the gradient of the T field is determined by the least square method. I have created a matrix ...

For the qr factorization using classic Gram-Schmidt algorithm, I found the 2 different implementations below. The first one uses the for loop to compute the upper ...

I write a simple MATLAB code for solving solid FEM problem. The problem looks like that (1) (2) x-------x | / | | / | | / | x-------x (3) (4) ...

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,...

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...

This question is more oriented around suggestions for simulation tools and how to approach simulating an object in orbit. So high level I am trying to simulate the concept of a Sky Hook. What are the ...