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11 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, ...
1
vote
0answers
16 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
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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
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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?
0
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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 ...
5
votes
1answer
36 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 ...
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. ...
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 ...
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 ...
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
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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 ...
4
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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
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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 ...
3
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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 ...
6
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0answers
88 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
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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
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 ...
1
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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....
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 ...
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 ...
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 ...
0
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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 ...
-1
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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 ...
3
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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 ...
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
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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 ...
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 ...
0
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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 ...
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 ...
3
votes
0answers
65 views

The implicit form of a NURBS curve

I am trying to evaluate and analyse a NURBS curve to generate a mechanism. I understand that the general form of a NURBS curve is commonly written as a parametric equation in the form of $f_{par}(t)$. ...
-1
votes
0answers
21 views

how to unscramble a .wav file to find the actual voice?

this question is a bonus question for my HW, and it's supposed to be something I am suppose to look up to solve. However, I have no idea what to look up on here to help me write this code. Can anyone ...
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
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0answers
38 views

Normalizing the right-hand side in Jacobi-preconditioned conjugate gradients

I have been reading the following paper: CG versus MINRES: An empirical comparison. In it a conjugate gradient solver is applied to a system matrix $A$ Jacobi-preconditioned on both sides. ...
1
vote
1answer
45 views

Importance Sampling for multidimensional integrals and random numbers from multivariable pdf's

I am aiming to get a numerical value for a five-dimensional integral using Monte Carlo Integration. I am getting good results using the Mean Value Method, but I would like to try to use Importance ...
1
vote
0answers
33 views

Digital beamforming: how payload manipulation can change beam direction without manipulating the carrier?

I'm interested in how digital beamforming works and I can not find an answer for a lot of time. I googled, asked teammates, and couldn't get it. Let me describe my question. From my understanding, the ...
3
votes
1answer
105 views

Multi threaded finite element assembly implementation

What is typically the best way to multi thread the assembly loop in a finite element code? Does anyone have experience with implementing this, that they can share? I can think of a couple of ways of ...
1
vote
0answers
37 views

Is there a way to generate a sample $(X_i, Y_i, Z_i)$ from custom distribution?

I'm newbie here. I'm wondering if it's possible to generate $(X_i, Y_i, Z_i)$ from my own distribution function? I know that there is a way to make own class for 1D variable. But what about 3D case?
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 ...
6
votes
1answer
138 views

General approach to infinite sums

My question is specific to algorithms and models of computation. I would like to write code to evaluate the following expression quickly and accurately: $$\log \left( \sum_{i=1}^{\infty}{I_{\nu+i}(2\...
0
votes
0answers
64 views

Numerical Partial Differentiation Check

In my computer vision course, we are working on extracting a 3D surface from a chain of 2D images taken under several conditions. This procedure is known as Photometric stereo. Prior to extracting the ...
6
votes
0answers
84 views

What is the best method to do a MC Integration of a multidimensional integral where the integration limits depend upon other variables?

What is the best method to do a Monte Carlo Integration of a multidimensional integral where the integration limits depend upon other variables? I am interested in getting a numerical value of a 5 ...
2
votes
1answer
79 views

Difference between asymptotic and non-asymptotic convergence in optimization?

I am reading some optimization methods and I am facing some issues with two terms "asymptotic and non-asymptotic convergence". What is the difference between them?
1
vote
0answers
25 views

How to identify the most different short sequence from a corpus that does not occur?

I would like to generate the most unique string (20 long, primer) of a defined length that does not occur in a much larger string (6.4 billion long, human genome). Of course, there could be many ...
1
vote
0answers
56 views

Good non oscilliatory derivatives for an exsisting grid

I'm calculating the entropy production of a shockwave by utilizing the equations: \begin{equation} \sigma = J'_q\frac{\partial}{\partial x}\left(\frac{1}{T}\right) +\frac{1}{T}\frac{4\eta}{3}\left(\...
2
votes
1answer
80 views

Implicit integrator for ODE with quadratic right-hand side

I have an ODE for an unknown $x(t):[0,\infty)\to\mathbb R^n$ of the following form: $$ x_i'(t)=a_i^\top x(t) + x(t)^\top Q_i x(t), $$ for $i\in\{1,\ldots,n\}$. Here, the vectors $a_i\in\mathbb R^n$ ...
1
vote
0answers
41 views

Convergence of Fourier series on subinterval with data matching at discrete node set

I am numerical analyst, and want to prove a result I observe numerically. Let $f$ be a periodic function on $I = [-\pi,\,\pi]$ that is $q$ times continuously differentiable, with the $(q+1)$th ...
3
votes
0answers
85 views

PETSc-like library for Julia

I want to build an application for Material Point Method (and probably other meshfree methods too) in Julia and I am looking for library for direct and iterative solvers that can help me with it. One ...
5
votes
0answers
70 views

Is this a legit way to sample a random matrix spectrum?

In order to undergird a theoretical model concerning many body physics, I want to have exponentially large eigenvalue spectra from the random matrix GOE ensemble. its properties are mainly (i) a ...
0
votes
1answer
66 views

Lagrange multiplier for boundary conditions in pure Neumann problem

I'm trying to solve $-u''=\cos(2 \pi x)$ with boundary conditions $u'(0)=u'(1)=0$ and the constraint $\int_{0}^1 u = 0$ I have to use linear finite elements, so let's assume that I have $M$ degrees of ...
0
votes
1answer
127 views

Intuition for relative error for vectors

I'm trying to understand the notion of relative error for vectors in $\mathbb{R}^n$, but it's not "clicking" somehow. $$\operatorname{\varepsilon-rel}(x_\text{approx}, x) = \frac{||x_\text{...

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