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What is the meaning of triangles color in the result of Tipping Problem in scikit-fuzzy (fuzzy logic)?

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 ...
17 views

Is it possible to use a fixed point iteration for solving this nonlinear system?

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} \\ u(x_{R}) &= g_{2} \end{...
403 views

Is there any open-source code for a hybrid 2D mesh (triangles and quadrilaterals)?

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 ...
11 views

Is there any reliable free/open source tool for structured mesh smoothing?

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 ...
78 views

Is there a Python version of the ODE tool pplane?

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 ...
15 views

How do you correctly implement Scipy's FFT procedures to produce a low-pass filter - image processing

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 ...
885 views

Higher precision floating-point arithmetic in numerical PDE

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 ...
27 views

3D Cooley-Tukey FFT

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 ...
336 views

When do not use preconditioners for sparse linear system of equations?

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 ...
74 views

Roundoff errors in FEM computations - generalized eigenvalues

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 ...
101 views

Algorithms for computing winding numbers of 2-sphere maps

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 ...
72 views

FEM : energy minimization VS PDE solving

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 ...
21 views

2D DFT for lower frequencies only; is there something significantly faster than numpy.fft.fft2 (throwing away high frequencies)?

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....
172 views

Solve non-linear equation in R

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 ...
168 views

How to avoid gsl root finder evaluate function outside its domain

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 ...
283 views

Global to local transformation matrix in 2D frame structures

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 ...
70 views

Regularisation of ill-conditioned matrix-vector problem

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 ...
3k views

What can a computational scientist do in the fourth industrial revolution?

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 ...
71 views

Computing eigenvalues of Schrodinger equation with spin

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 ...
255 views

Is there a simple way to avoid carbuncles for FD WENO methods?

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 ...
112 views

How to compute the Eigenvalue and Eigenstates of Quantum well with Effective mass using finite difference method in Python?

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/...
34 views

Null Christoffel symbols associated to the FLRW metric obtained via Mathematica [closed]

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 ...
1k views

Split-step Fourier method applied on Schrodinger equation

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 ...
55 views

Two-dimensional ordering issue – alternate sort order ascending/descending to reduce fluctuations - trivial?

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 ...
545 views

31 views

Help with debugging block GMRES

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 ...
185 views

Implementation of Z^2 error estimator in Abaqus for adaptive mesh refinement

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 ...
42 views

State change of input-output system

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 ...
106 views

Fitting line to a staircase function

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 ...
262 views

Is it possible to partition 2D data into bins such that each bin contains the same number of samples?

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 ...
72 views

Backward Euler + Quasi Newton(Broyden) method fails to solve Van der Pol's equation(Stiff ODE)

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 ...
17 views

If L is regular so is collapsing doubles [closed]

Suppose L is a regular language. I need to prove that $$L'=\{x_0\cdots x_n:x_0x_0x_1x_1\cdots x_nx_n\in L\}$$ I thought I could take a DFA which computes L, and take each accepting state, together ...
1k views

Tanh-sinh quadrature numerical integration method converging to wrong value

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

Different sources of error in Finite Element computations

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 ...