All Questions

I want to simulate the hyperbolic partial differential equation $$W_{tt} + V W_{tx} + k_E V W_x + k W_t = 0,$$ but I am having trouble finding a discrete analog of this equation which is numerically ...

Any literature that extensively discusses the ability to strongly interpolate computationally on little empirical data? This topic has fascinated me, but I find that it seems a bit novel. Particulary, ...

The dmDisplayFrequency in DEVMODE appears to be the vertical {Wikipedia} refresh rate for the monitor- does that necessarily correspond to the ...

see my question over here: https://stackoverflow.com/questions/69706672/use-biconjugate-gradient-with-incomplete-lu-decomposition-as-preconditioner What can I do to solve this problem?

For the past couple of days, I have been thinking a lot and searching online for an algorithm capable of estimating the number of Self-Avoiding Walks (SAW) of length $n$ in $\mathbb{Z}^2$. There is a ...

Suppose I have a triangular element with vertices ${\vec{r_1},...,\vec{r_4}}$ and a function $f(\vec{r})$. I want to calculate the fourier integral over this triangle such that: $$F(k_x,k_y)=\int \int ...

I have always taken for granted circuit simulators and I didn't spend time understanding now. I wish to understand better now. Normally when you forward simulate ODE systems there is a single dynamic ...

I did this simple analysis on RFEM, of a rigid-supported beam loaded with a point moment. Before analysis, I didn't assign any kind of mesh manually. When I turn on the FE Mesh visible on Project ...

I have the two following algorithms for GMRES(m) and left preconditioned GMRES. GMRES(m) Left preconditioning I would like to know if anyone could explain why steps 10 through 12 are not used in the ...

I am looking for some LBB-stable velocity-pressure combinations for incompressible Navier-Stokes where the pressure space is element-wise discontinuous, preferably with a linear variation elementwise. ...

I am currently solving the harmonic equation using a P1 FEM discretisation. The resulting matrix $A$ is SPD and fairly sparse so I use a preconditioned conjugate gradients (CG) solver to find a ...

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 am now working on solving MHD equations with finite difference method, which include nonlinear equations: $$ \frac{\partial\rho}{\partial t}+\nabla\cdot\left[\left(\rho_0+\rho\right){v}\right]-\...

Is there an efficient way to numerically compute Stirling numbers of the second kind? An approximate (not exact) method would suffice. Something similar to the connection between factorials and gamma ...

I have been using Pointwise for grid generation and found the quality of smoothed grids to be stunning. I am not aware of any free/open source alteranative that offers the same capabilities for ...

Consider the following differential equation \begin{align} \frac{\partial f(u)}{\partial x} &= g(x), \ \ x\in [x_{L},x_{R}] \label{Eq2.2} \\ u(x_{L}) &= g_{1} \end{align} where $f(u)$ is a ...

I am following this example https://scikit-fuzzy.github.io/scikit-fuzzy/auto_examples/plot_tipping_problem_newapi.html from documentation of scikit-fuzzy library,but I have a question in the figure ...

The question is pretty much the title. Note that I have lots of experience using open-source meshing tool, e.g. Gmsh and OpenFoam blockMesh & snappyHexMesh. Nevertheless, I have no idea on how to ...

This is the same question as this one, except for Python instead of Mathematica. Basically, the MATLAB software pplane is a staple in ODE courses. Is there a Python equivalent? Sample outputs from ...

I'm following this low-pass filter example in the text "Image Operators: Image Processing in Python 1st Edition" by Jason M. Kinser, but can't seem to duplicate their results. The text's ...

I have the impression, from very different resources and talks with researches, that there is a growing demand for high precision computations in numerical partial differential equations. Here, high ...

To compute the $N$-point DFT $$ X[k] = \sum_{n=0}^{N-1} x[n] W_N^{kn} $$ where $N = N_1 N_2$, we can write the indices as $n = N_2 n_1 + n_2$ and $k = k_1 + N_1 k_2$, (effectively packing the data ...

I'm implementing a solver of Finite Element Method, and to solve the linear system of equations I'm using gmres from MKL of Intel. Exists the option with and without a preconditioning. In what case it ...

This is a continuation of my previous question. I am trying to effectively compute a bound for the roundoff errors in some FEM computation (2d polygons, triangular meshes). Below I will write some of ...

I have a question concerning computational geometry which arises in the simulation of fields with topological defects, and I'd like to know whether there's an efficient algorithm (or any algorithm) to ...

Engineering FEM When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as: Multiply your PDE with a test ...

I do a lot of 2D discrete FFT in python using np.fft.fftshift(np.fft.fft2(y)), then throw away 90% or more of the array, keeping only the central low-frequency area....

I need to solve the following equation for $x$ in [0, 1]. Assume $0<\alpha<1$ and $0<\lambda$. $$(1 - x)^{\alpha+1} - \lambda (x+1)^{\alpha+1} = -2\lambda (\alpha + 1) x^\alpha$$ Would very ...

When I use the newton's method or hybrid solver in the GSL package to deal with 1-D or multidimensional root solving problems, the code frequently crashes when the solver requests function value ...

In section 3.2 of this paper [1], where 2D planar frame structures are being analyzed, the authors mentioned a transformation matrix to be used in extracting the element displacement vector from the ...

I have a linear* problem which arises from an integro-differential system, and writes: $$ (\mathbf{I}+\lambda \mathbf{A})x = b $$ where $\mathbf{A}$ is a real full matrix, size $n\times n$, but is not ...

This question is neither scientific nor technical but more career related. I am at a junction in my professional life where I need to make a decision with regard to the future of my career. At the ...

I want to solve a 2-dimensional particle in box problem with two electrons in the quantum well.I would like to take into account spin of electrons and Coulomb interactions to compute singlet and ...

I have implemented finite-difference WENO scheme for Euler equations (with some variants - WENO-JS, WENO-Z, WENO-M, different flux splitting). It works well, but have problem with so-called carbuncles ...

I want to compute the eigenvalues and eigenstates of a quantum well with different effective masses of electron in the barrier and in the quantum well. As can be seen [1]: https://github.com/mholtrop/...

I'm trying to make a mathematica notebook that computes the Christoffel symbols associated to the Friedmann-Lemaître-Robertson-Walker metric (noted FLRW in the notebook) describing an homogenous and ...

I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...

I have a solution in search of a problem that some of you could perhaps help me with. Let $L$ be a list of elements. Each element has two inherent properties/attributes ($a$, $b$) that can each be ...

I'm very new to computational Physics and am finding conflicting statements on whether the velocity Verlet algorithm, defined as: $\begin{align} x_{n+1} &= x_n + v_n \Delta t + \frac{1}{2} a_n \...

I often hear that cell centred finite volume is second order accurate but at the same time I come across notions of high order FVM flux schemes. Is there a distinction between the two? If I were to ...

Issue description I am working on human brain tACS simulations where I have the models of the skin, skull, csf, brain and ventricles in STL format. The shape does not matter and there are no ...

Consider the Laplace problem: \begin{align} -\nabla^2 u = f \qquad \text{in } \Omega \\ u = 0 \qquad \text{on } \Gamma \end{align} The weak problem is find $u_h \in V \subset H^1$ such that $\...

I have written block version of GMRES by referring [1] and MATLAB implementation of gmres. I need to write it for complex matrices. My block implementation when run on single RHS is giving correct ...

Currently, I am working on a remeshing routine for my simulations (Abaqus 6.14-1) using python scripts. The simulation deals with the Brinell indentation test and as the remeshing software I use Gmsh ...

Edited Given a computer model $F:\mathbb{R}^3 \to \mathbb{R}$, with inputs $x, w$ and $z$, and output $y=F(x,w,z)$, where for any input, we are able to evaluate the output, my goal is to tune the ...

I have a staircase/step function $n(E)$. I know the points $\{E_i\}$ at which each "step" occurs and all steps are of constant height 1. I need to fit a line $a + bE$ to this function and ...

I am trying to sort data following a bivariate distribution into a numpy histogramdd, where each bin should contain the same number of data points (to the nearest whole sample). I expect that some ...

The first guess is using the forward Euler approach. The first jacobian is using finite differences. Then NR method is used to solve for the next iteration and Broyden's method is used to update the ...

I'm trying to write a Python program to use Tanh-sinh quadrature to compute the value of \begin{equation} \int_{-1}^1 \frac{dx}{\sqrt{1-x^2}} \end{equation} but although the program converges to a ...

Consider the problem $-\Delta u = f$ in $\Omega$, with $u=0$ on $\partial \Omega$. Suppose that $\Omega$ is a polygon and that we approximate the solutions to the previous problem using Lagrange ...