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Constructing Mesh In FreeFem++

I am new to building 3D meshes in FreeFem++. Is it possible to build the mesh below? The domain is 1+1/8 in length, 1 height, and 1 width. There is a 1/4 depth and 1/8 wide channel that cuts though it ...
FluidMan's user avatar
1 vote
0 answers
12 views

Numerical calculation of Lyapunov exponents using SciPy's built-in solve_ivp

I have previously successfully implemented the QR decomposition method in MATLAB to calculate Lyapunov exponents for Lorenz equations. See here. This method integrates the stacked system, i.e. the ...
Axel Wang's user avatar
  • 105
3 votes
1 answer
357 views

In linear programming, is there a way to constrain two variables to not have opposite sign

Say I have two sets of variables $x$ and $y$ of equal size. $x$'s have a lower bound $x_{min}<0$, and $y$'s have a lower bound $0$. Is there a linear way to constrain that $x_i\geq0$ if the ...
jf328's user avatar
  • 438
0 votes
0 answers
17 views

Discretization of 2D advection equation with non-constant speed

Suppose I have a 2D advection equation $$\frac{\partial \rho}{\partial t}=-\nabla\cdot(\vec{w}\rho)$$ with $\vec{w}=(u,v)$ non-constant and having zero divergence. I want to numerically solve this ...
KnobbyWan's user avatar
  • 101
0 votes
0 answers
21 views

How to use a custom OdeSolver in Scipy's solve_ivp

In Scipy's solve_ivp documentation, we see the method argument can be either a string or a user-defiend OdeSolver inherited from ...
Axel Wang's user avatar
  • 105
1 vote
1 answer
74 views

accuracy problem for a null space calculation on a sparse rectangular matrix

I have been using the QR-based approach on this link to find the null space of rectangular matrices, and possibly sparse matrices, that emerge as a result of some coupling conditions of different ...
Umut Tabak's user avatar
-1 votes
1 answer
39 views

Gmsh problems in Google Colab, visualize mesh

I'm trying to implement mesh in Google colab from gmesh tutorials. I have an error: Exception: Fltk not available My code is: ...
Malinamalina's user avatar
1 vote
1 answer
63 views

Numerically computing envelope of Gibbs oscillation

If I numerically compute the envelope of $\sin(\pi t)$ using a Hilbert transform, I obtain exactly what I expect: If I do the same for $\mathrm{sinc}(t)$, still I obtain an envelope which agrees with ...
user14717's user avatar
  • 2,145
2 votes
1 answer
146 views

Where am I making a mistake in solving the heat equation using the spectral method (Chebyshev's differentiation matrix)?

I would like to numerically solve the following heat equation problem: $$ u_t = \Bigg(2{a \over l}\Bigg)^2 u_{xx} \tag 1$$ $$ x \in [ -1, 1 ] \tag 2$$ $$ u(x, 0) = 0 \tag 3$$ $$ u(1, t) = A \sin \Bigg(...
Nikola Ristic's user avatar
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0 answers
49 views

ENO-Runge-Kutta discretization

One beginner's question about discretization of a Hamilton-Jacobi equation(non-linear) $$ u_t = H(u_x) $$ $u_x$ is discreated with 2nd order ENO-FD 1st order: $D_1^{\pm}u = \pm [u_{x\pm1} - u_x ] / \...
solanin's user avatar
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0 answers
24 views

Help with inferring Network topology from Spectral templates

I am trying to use matlab and YALMIP to solve a graph learning problem of recovering eigenvalues from the eigenvectors of the covariance of sampled graph signal data. This is to implement the ...
user86422's user avatar
0 votes
0 answers
24 views

Recommendations for some new books about computational contact mechanics in solid mechanics

I want to simulate some frictional contact problems, but I'm not familiar with this field, could you please recommend some new books as introductions?thank you
吴yuer's user avatar
  • 151
1 vote
0 answers
50 views

Overlap matrix and its inverse matrix

Now, we consider a non-orthonormal basis: $$\mathcal{S}_N=\{|\alpha\rangle,a^\dagger|\alpha\rangle,a^{\dagger 2}|\alpha\rangle,\ldots,a^{\dagger N}|\alpha\rangle\},$$ where $|\alpha\rangle$ is the ...
Young Q's user avatar
  • 11
0 votes
0 answers
43 views

3D Quadrature schemes with points on boundary

In one dimension there are two types of quadrature schemes. asymmetric rules like Newton-Cotes like formulas (Trapezodi, Simpson), and Clenshaw-Curtis place sampling points on boundary of the ...
Prokop Hapala's user avatar
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0 answers
35 views

Methods for delaying the "break" in non-linear least squares optimisation when the step size gets too small?

I am using the Levenberg-Marquardt method for calibration purposes. Typically, the RMSE of my calibration looks like: I want to break the algorithm when the algorithm step-updates start to slow down, ...
THAT'S MY QUANT MY QUANTITATIV's user avatar
0 votes
1 answer
75 views

Are there any established direct eigensolvers for sparse hermitian matrices?

I have experience with LAPACK (direct solvers) and ARPACK (sparse iterative solvers), but are there any sparse direct solvers? I am concerned more with preserving space than with fast solutions. ...
DJames's user avatar
  • 405
0 votes
0 answers
38 views

Which numerical method can I use to solve this system of hyperbolic PDEs?

Backround The mathematical model I am trying to numerically solve models wave propagation inside a cylinder with specific material properties suited for dynamic loading. The cylinder's upper base is ...
Nikola Ristic's user avatar
1 vote
1 answer
45 views

Finding the Vector $v$ for a Given Householder Matrix Transformation of Non-Collinear Vectors $a$ and $b$

Consider a vector $v$ in $\mathbb{R}^{n\times1}$. The Householder matrix is defined as follows: $$H(v)=I-\dfrac{2vv^T}{v^Tv}.$$ It can be demonstrated that $H(v)$ is symmetric and orthonormal. The ...
Ilkay Burak's user avatar
2 votes
1 answer
76 views

Solving for $X$ in $\sum_{a,b} b a^T b^T X a = Y$

Suppose I have $k$ pairs of $(a,b)$ where $a$ and $b$ are vectors in $\mathbb{R}^d$, $Y$ is $d\times d$ and I need least squares solution for $X$ in the following $$\sum_{(a,b)}^k b a^T (b^T X a) = Y$...
Yaroslav Bulatov's user avatar
0 votes
0 answers
49 views

eigenvalues of inhomogeneous Helmholtz equation violate superposition using FEM

I am trying to solve the in-homogeneous Helmholtz equation with damping and forcing using finite element method (FEM) with FEniCSx. The equation is; $c^2\nabla^2p - c^2\omega i d \nabla^2p + \omega^2 ...
Ekrem Ekici's user avatar
1 vote
1 answer
139 views

Solving PDEs using FEM using cubic Hermite polynomials

everyone. I am a beginner in Numerical mathematics, I have some idea of how to use Galerkin method to solve PDEs numerically, but so far I had no luck finding an example of how to solve a simple PDE ...
Nurbek Saidnassim's user avatar
0 votes
1 answer
96 views

Step size constraint in Euler backward

I am dealing with an assignment in MATLAB. It has to do with 'self-driving' cars which are driving in-front/behind eachother. Assuming M cars on a single-lane road, each car adjusts its speed based on ...
user46892's user avatar
2 votes
1 answer
128 views

Large set of nonlinear equations in Sympy

I have a set of 6 nonlinear equations, and using Sympy I find the values of the 6 unknowns. This works perfectly and it directly gives the exact solution, using sympy.solve to be specific. Now I ...
je2703's user avatar
  • 21
5 votes
2 answers
438 views

Number of function calls and jacobian calls in scipy.root

Just as an exercise, I am numerically solving the following system of equations: $$ \begin{equation} \begin{cases} x^2 + y^2 = 32 \\ 3x + 7y = 15 \end{cases} \end{equation} $$ ...
Tarik's user avatar
  • 173
2 votes
1 answer
89 views

references for optimization in the context of parameter identification with finite elements

i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements. My optimization problem is a non-linear least squares data-...
Simon's user avatar
  • 123
3 votes
1 answer
244 views

Finite difference problem

I have a problem to resolve with the Finite Difference method in $[a,b]$: $$-\frac{d}{dx}(\alpha(x)\frac{du}{dx})= g(x),$$ with $\alpha(x) \in L^{\infty}$ continuous in $]a,c[$ and $]c,b[$ and ...
Kaneki Ken's user avatar
3 votes
0 answers
70 views

How is the Alternating Schwarz Method used as a Preconditioner to a Krylov Method?

I am reading "Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations" (Smith 1996), and I am confused as to how the below Alternating Schwarz algorithm ...
Jared Frazier's user avatar
1 vote
1 answer
86 views

Symmetry axis boundary condition

I was wondering about the symmetry axis boundary condition in commercial CFD solvers such as ANSYS Fluent. If the problem is the flow through a round pipe or out of a round nozzle, it is natural to ...
Natalie Leggera's user avatar
2 votes
1 answer
156 views

Solving non-linear partial differential equation numerically: $u_{xx}+u_{yy}=\mathrm{e}^{u}$

To start with, I need to solve this partial equation numerically, but I do not know how to do that. If I try a finite difference method, I face a problem that $u_{i,j}$ is also located in exponential, ...
Evgeny's user avatar
  • 21
2 votes
1 answer
113 views

How to formulate a convex expression to minimize the difference between Frobenius norm of a positive semidefinite matrix and a positive value

So what I am trying to do is to minimize the distance between the Frobenius norm of a PSD matrix and a real positive value, which can be formulated as $$\min \left|\|\textbf{P}\|_F - J\right|^2$$ ...
tyrela's user avatar
  • 21
2 votes
0 answers
42 views

How to use a preconditioner estimated from a subset of data?

Suppose I'm solving $Ax=b$ using row-action method like Kaczmarz for $m\times n$ matrix A with $m\approx \infty$ and have $H_k=\frac{1}{k}A_k^T A_k$ which is an estimate of the Hessian obtained from ...
Yaroslav Bulatov's user avatar
3 votes
1 answer
185 views

Solving underdetermined Lyapunov equation?

I'm solving the following for $X$ with $A,B$ singular positive semidefinite matrices. $$AX + XA = B$$ Because $A$, $B$ are singular, standard Lyapunov solver fails However, if I heuristically skip ...
Yaroslav Bulatov's user avatar
0 votes
1 answer
44 views

draw a log-log plot of MSD (mean square displacement) versus `t` of a movement of the polymer chain

Cross-posted on MMSE (Matter Modeling Stack Exchange). The following are the movements of the center of mass of a polymer chain over time in a monte carlo simulation. ...
user366312's user avatar
1 vote
2 answers
96 views

Implementing matrix term version of Gauss-seidel

I am trying to implement the below description from Ch. 11 of Heath's "Scientific Computing An Introductory Survey" of the Gauss-Seidel iterative method for solving a system of linear ...
Jared Frazier's user avatar
0 votes
1 answer
67 views

How to plot the power spectrum

I have an array of data whose columns are solution vectors to a system of ODEs at a specific time. I want to plot the power spectrum of a solution at a specific time, but when I attempt this I get ...
KZ-Spectra's user avatar
5 votes
0 answers
114 views

Single precision vs double precision conjugate gradients

I tested my conjugate gradients implementation with float and double precision and contrary to my guess the double code was twice faster than the single precision code. The reason is that I need many ...
lightxbulb's user avatar
  • 1,271
0 votes
0 answers
12 views

Simulating a dataset from model output when model includes multiple binary deviation-coded variables

I am trying to simulate data using parameters from a glmer() model output. The model, which comes from a published paper, is as follows: DV ~ 1 + group* sex *verb type + trial number + (1 |participant)...
HungryHippo's user avatar
2 votes
0 answers
57 views

Numerical integration in Fourier space over 3D grid

I am attempting to implement a model outlined in this paper: General magnetostatic shape–shape interactions Background This model allows the calculation of magnetostatic interaction energies between ...
JasonC's user avatar
  • 31
4 votes
0 answers
120 views

FVM for non-regular domain with triangular mesh

Setup The 1D convection-diffusion equation is given by: \begin{equation}\tag{1} \frac{\partial u}{\partial t} + v \frac{\partial u}{\partial x} - \mu \frac{\partial^2 u}{\partial x^2} = 0, \end{...
VIVID's user avatar
  • 91
0 votes
0 answers
81 views

A confusion about the bubble function in lumped mass FEM

I am studying knowledge related to lumped mass finite elements. As is well known, lumped mass finite element methods higher than 2nd order on simplex mesh require the construction of new function ...
Owen Jun's user avatar
0 votes
0 answers
46 views

Is a sort of "z-drift" the result of numerical precision errors in FDM?

Upon solving the 2D wave equation with Neumann boundary conditions $u_x = u_y = 0$ on a rectangular $10 \times 10 \times 10$ grid, I noticed something odd - $u$ seemed to shift upwards with time. This ...
JS4137's user avatar
  • 133
1 vote
1 answer
83 views

Adding a diffusion term to the MUSCL - Kurganov and Tadmor central scheme

Im currently using a MUSCL scheme with a rusanov flux and Van Leer limiter to simulate the 2d euler equations: $$ \frac{\partial \rho}{\partial t} + \frac{\partial \rho v_x}{\partial x} + \frac{\...
user46777's user avatar
1 vote
0 answers
42 views

Solution to the Liouville-Gibbs equation

What would be the approach to numerically solve for $\rho(x,t)$ the following equation with some initial conditions $$\frac{\partial\rho}{\partial t} +\sum_{i=1}^n\left(\frac{\partial(\rho g_i)}{\...
homocomputeris's user avatar
0 votes
1 answer
53 views

Local truncation error of given implicit 1-step scheme

I'm given the 1-step implicit scheme $$y_{n+1} = y_n + \frac{h}{6}[4f(t_n, y_n) + 2f(t_{n+1}, y_{n+1}) + hf'(t_n, y_n)],$$ where $y'(t) = f(t, y)$, and I'm seeking the scheme's local truncation error. ...
jackyooo's user avatar
1 vote
0 answers
35 views

Implementation of operator splitting method for Wigner equation

I am dealing with the integro-differential equation for Wigner function, $$\frac{\partial f}{\partial t}+p\frac{\partial f}{\partial x}+\\+\frac{1}{\chi}\left\{\int_{-\pi}^{+\pi}dy\,\int_{-\infty}^{+\...
Artem Alexandrov's user avatar
3 votes
1 answer
175 views

Stability of Euler forward method

I am trying to solve a linear system of ODEs of the form: $$ \frac{du}{dt} = A u, \quad u(0)=k$$ where $A$ is a 2x2 matrix and $u(t)$ is a 2x1 column vector. I want to solve this numerically, using ...
rainbow's user avatar
  • 31
0 votes
0 answers
26 views

Doubt of wavelets about the return of comand plot() of package Wavethresh in R language

I take a plot of father wavelet with this code library(wavethresh) y <- c(1,1,7,9,2,8,8,6) ywd <- wd(y, filter.number=1, family='DaubExPhase') plot(ywd) But ...
Siqueira's user avatar
1 vote
1 answer
116 views

Calculating Hypergeometric1F1 for large arguments

Cross posted on StackOverflow I am trying to use the gsl library for calculating 1F1. I have some C code. The following works and matches Mathematica's results for ...
user3236841's user avatar
0 votes
0 answers
16 views

How do you determine the Mott-Insulator to Superfluid transition in the Bose Hubbard System

I am doing some simulations on various systems expressed in 2nd quantization and one of the points of interest of mine was Phase transitions in the Bose-Hubbard model $$ H = \sum_{k} \{ t_k(b^\dagger_{...
Mephistopheles Faust's user avatar
1 vote
1 answer
82 views

derivative matrix and the Dirac delta distribution

For a project I'm working on, I was working with the following equation $$ w(x) = \int k(x,y)v(y)dy $$ I noticed that if I choose $$ k(x,y) = -\delta'(x-y) $$ Then we probably get (I haven't touched ...
NNN's user avatar
  • 668

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