All Questions

I have the following functions in an optimization problem. $x\times 2^{(y/x)-1}$ $ x \log (a+b\times 2^{(y/cx)-1} )$ Here, x,y>0, and also a,b,c>0, and b>a. For these conditions, I checked ...

https://stackoverflow.com Krylov solvers for iterative computation of the smallest singular value and the corrensponding singular vectors of a matrix Edit: This is a follow-up question to How to ...

For stable time steps for the RKDG method for transport equations we require that $$ \Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|}, $$ where $\lambda$ is the eigenvalue of our conservation law ...

I have a set of linear equations, $Ax=b$. And about half of the elements in the right-hand side (vector $b$) are equal to zero. My system matrix $A$ is a sparse complex matrix. And $A$ is in the size ...

I am working on a problem with very large sparse matrices. I'd like to compute $A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of $A$ is 2E+5 x 2E+5 ...

I wish to compute $$ \frac{1}{1 + \frac{1^3}{1 + \frac{2^3}{1 + \frac{3^3}{1+\cdots} } } } $$ to high accuracy. To start, I tried computing $$ \frac{1}{1 + \frac{1^2}{1 + \frac{2^2}{1 + \frac{3^2}{1+\...

I am trying to use scipy.optimize to solve a minimizaiton problem but getting failures on using an inequality constraint or a bound. Looking for any suggestions regarding proper usage of constraints ...

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...

Given an $m \times n$ matrix $A$ and a vector $x\in\mathbb R^n$, with $m<n$, what's an efficient way of computing the projection of $x$ onto the kernel of $A$?

I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...

About the flexible GMRES (fgmres), we know that it is a variant of right preconditioned gmres. And the robust command gmres in matlab as follows: ...

I am using Maxima to check whether a given sequence is diverging to $+\infty$. I know that this problem is undecidable and we note that Maxima is throwing an error: ...

I have a saddle-point system of the form \begin{equation} \begin{bmatrix} A & B \\ B^T & O \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} f \\ \vec{0} \end{bmatrix}, \end{...

I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...

I'm trying to study the relationship, if any, between the accuracy of a federated learning network and the number of attacking sybils. In order to do this, I need to create a simulated FL network and ...

I have to integrate expression f(x) * g(x) for many different functions f but just one g. I ...

I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...

The following relates to the linked question: Scattering of waves in a symmetrical potential (using python) I have attempted to solve the problem for $U(r)$ using ...

Consider the following integrals $$ I_1(x) =\int_0^\infty\mathrm dy \frac{F(x + \mathrm iy) − F(x −\mathrm iy)}{\mathrm e^{2πy}-1}, $$ And $$I_2(x) =\int_1^x F(t)dt$$ Where, $ F(z) = \sin^2[π\Gamma(z)/...

I am trying to obtain the weak form of the Navier-Cauchy equation, which is $$- \rho \omega ^2 \textbf{U} - \mu \nabla ^2 \textbf{U} - (\mu + \lambda) \nabla (\nabla \cdot \textbf{U}) = \textbf{F}$$ ...

Im trying to implement a frequency-domain filter in python using an specific response function. The idea is to perform the Fourier transform of an image multiply it by the filter response function and ...

I have a coupled set of PDEs that need to be solved as part of a larger problem. I am currently approaching this by computing spatial derivatives with finite differences and using PETSc's nonlinear ...

I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...

I am a physics undergrad and I have MOKE data for a magnetic material (thin permalloy film on a silicon substrate). Here is one of the hysteresis loops I obtained, plotted using Python: The form of ...

I am trying to run a software package developed that has some dependencies such as numpy on a cluster. My issue seems to be with the python environment. I have set up the environment correctly for ...

I'm solving an elastic homogenization problem and I'm having problems with mesh artifacts. I would like to first give a brief summary of what I do: I have a system with inhomogeneous (but isotropic) ...

Is there an iterative solver that can handle potentially zero entries on the central diagonal? I am implementing a polynomial fitting algorithm (up to $10^{th}$-order) and my matrix is a "...

I am trying to simulate the propagation of a gaussian beam through a lens using an FFT approach. I tried to implement the approach described by Couairon in this paper at page 43: https://link....

I have a system of 4 nonlinear 1st-order PDEs. I want to solve them numerically by method of lines, first discretizing space. This leads to the system of $N\times 4$ coupled ODEs. $$ \mathbf{u}_{i} =...

I'm looking for a method to solve a 20000 variable, 20000 residual non-linear PDE with a Galerkin method. I have Fortran subroutines for: The residuals: $\vec{r}(\vec{x})$; Their Jacobian multiplied ...

I’m trying to write the weak form of the Navier-Cauchy equation in the component form, where $u_1$ and $u_2$ are the displacement components: $$-(2 \mu +\lambda) \frac{\partial ^2 u_1}{\partial x_1 ^2}...

Which one is better: FORTRAN or Python? And I guess that in both cases you need Gnuplot, am I right? I'm working on a Windows machine at the moment. I'd like to use it to get numerical solutions for ...

I have to solve the following PDE for a Call option : $\partial_tV + \{ \alpha - (\mu - \lambda/ \alpha -log(S))\}S\partial_SV + 1/2 \sigma^{2}S^{2}\partial_{S}^{2}V - rV = 0$ Where V(S,t) is the ...

What is the result of the method for multiple eigenvalues? Is there any case for which this method will not work altogether?

Are there $P0$ (zero degree/constant element) nonconforming methods for approximating solutions in $H1$? More specifically, I have the equation: $$u-f - T\Delta u = 0$$ Which can be interpreted as ...

I have no idea how a computer works on the lowest voltage moving through tiny circuit chips level, but if you wanna travel space from one star to another, don't you need a faster than light ...

Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$. Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located). Let ...

I want to simulate the propagation of a sinusoidal plane wave in a rectangular domain using Finite Elements Method. First, the wave should propagate through a fluid medium, then it will encounter a ...

I wonder why OpenFOAM code has its own data structures Lists, HashTables, ... etc. when there is the STL in C++? Another ...

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]-\...

I have a pretty naive question, though important to me. Usually when solving the following PDE in solute transport: $\frac{{\partial C}}{\partial t } = \nabla. (D\nabla C -vC )=0,$ one can be asked to ...

Background: I have only built one working numeric solution to 2d Navier-Stokes, for a course. It was a solution for lid-driven cavity flow. The course, however, discussed a number of schemas for ...

Let define a predictor step for the equation $\frac{\partial u}{\partial t}+\frac{\partial f}{\partial x}=0$, by: $$U_{i+\beta}^{n+\alpha} \equiv \bar{U}_{i}=U_{i}^{n}+\beta\left(U_{i+1}^{n}-U_{i}^{n}\...

I have a large system of boundary value problems of the form $$ \frac{d^2 y }{dt^2} = C(t) y + b(t), $$ where the variable $y$ is a vector that has anywhere from 50 to around 500 components, $C$ is a ...

Let $n = 10^6.$ Let $A \in \mathbb{R}^{n\times n} $ be the lower triangular matrix having 1's on and below the main diagonal. We want to solve the following linear system: $$ (A + uv^T)x = b$$ by the ...

I'm working with a Matlab codebase wherein I'm attempting to solve A*c = b by approximating the (square) matrix A with its ...

I am looking to make certain computations on the vertices of periodic cubic honeycombs and quasiregular honeycombs like tetrahedral-octahedral honeycomb. Cubic are simple enough and amount to generate ...

I am new to computer science and I was wondering whether half precision is supported by modern architecture in the same way as single or double precision is. I thought the 2008 revision of IEEE-754 ...

The Gauss-Kuzmin distribution gives the probability of an integer appearing as a partial denominator in the continued fraction of a real number $x$ as $$ P(a_k = k) = -\log_2\left(1 - \frac{1}{(k+1)^2}...

I was wondering how specific symmetries or constraints such as property-invariance transformation are imposed on any (deep) neural net when they are trained. I'll appreciate it if anyone can aware me ...