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0answers
17 views

Instability at the boundary of a finite difference simulation of a hyperbolic PDE

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 ...
0
votes
0answers
13 views

Any literature that extensively discusses the ability to strongly interpolate computationally on little empirical data?

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, ...
0
votes
0answers
9 views

DevMode, Videomodedescriptor: Screen Refresh Rate Data [closed]

The dmDisplayFrequency in DEVMODE appears to be the vertical {Wikipedia} refresh rate for the monitor- does that necessarily correspond to the ...
-1
votes
0answers
21 views

Use BIConjugate Gradient with incomplete LU decomposition as preconditioner [closed]

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?
5
votes
1answer
37 views

Estimate the number of self-avoiding walks of length $n$

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 ...
0
votes
0answers
34 views

Fourier integral over elements

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 ...
2
votes
2answers
70 views

How are consistency constraints maintained in Circuit Simulation?

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 ...
0
votes
2answers
23 views

How does RFEM give non-linear results with a two-node mesh?

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 ...
1
vote
1answer
60 views

Doubt regarding GMRES(m) and preconditioned GMRES

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 ...
3
votes
1answer
56 views

Discontinuous pressure elements for incompressible Navier-Stokes

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. ...
2
votes
1answer
88 views

Incomplete Cholesky preconditioner for CG efficiency

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 ...
-1
votes
3answers
310 views

Solving coupled ODEs using Runge-Kutta method

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 ...
2
votes
1answer
327 views

Solving nonlinear PDE with finite difference based on Newton-Krylov

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]-\...
6
votes
2answers
3k views

An efficient way to numerically compute Stirling numbers of the second kind?

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 ...
4
votes
0answers
66 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 ...
1
vote
0answers
79 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} \end{align} where $f(u)$ is a ...
-1
votes
0answers
35 views

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 ...
4
votes
2answers
427 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 ...
3
votes
2answers
92 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 ...
1
vote
0answers
22 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 ...
11
votes
2answers
900 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 ...
3
votes
0answers
32 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 ...
3
votes
1answer
363 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 ...
4
votes
1answer
80 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 ...
5
votes
1answer
102 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 ...
6
votes
0answers
89 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 ...
1
vote
0answers
24 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....
0
votes
1answer
188 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 ...
2
votes
1answer
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 ...
0
votes
1answer
284 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 ...
2
votes
0answers
78 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 ...
9
votes
4answers
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 ...
0
votes
1answer
88 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 ...
2
votes
1answer
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 ...
1
vote
0answers
118 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/...
-1
votes
0answers
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 ...
1
vote
1answer
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 ...
1
vote
2answers
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 ...
3
votes
2answers
548 views

Time Reversibility of Velocity Verlet Algorithm

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 \...
3
votes
0answers
47 views

What determines the order of a finite volume scheme?

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 ...
2
votes
1answer
91 views

Determining the voxels between two boundary surfaces

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 ...
1
vote
2answers
119 views

Why aren't face integrals for an element calculated in FEM but they show up in FVM?

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 $\...
0
votes
0answers
34 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 ...
2
votes
0answers
187 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 ...
0
votes
0answers
43 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 ...
1
vote
3answers
107 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 ...
0
votes
2answers
264 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 ...
4
votes
2answers
76 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 ...
7
votes
3answers
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 \begin{equation} \int_{-1}^1 \frac{dx}{\sqrt{1-x^2}} \end{equation} but although the program converges to a ...
2
votes
2answers
146 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 ...

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