All Questions

In an introduction to Discontinuous galerkin methods, I have some problems in checking the weak formulation. I'm looking at page 16 here The context is the advection reaction equation: $$\operatorname{...

Consider the Navier stokes equation after the discretization with conforming finite elements with source term $f=0$. We have the algebraic structure of a saddle point problem: $$M \dot{u} = f- Au -B^...

I have a nonlinear mixed-integer optimization problem, and because of very high complexity when solving it using methods like Branch and Bound, I resorted to solve it using alternating method and ...

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...

For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer. Can you recommend ...

I am trying to solve a differential equation in the form: dx/dt = funct(x) using scipy odeint. However, for some initial values, I get a "ODEintWarning: Excess work done on this call", even ...

Let $z, b \in \mathbb R^n$, $A \in M_n (\mathbb R)$ and $|z| := (|z_1|, \dots, |z_n|)$. I am searching for an efficient algorithm to solve the absolute value system: \begin{equation} z - A |z| = b. \...

I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this: Many practical problems of importance are non-convex, and most non-...

This question is a follow-up of this one. The weak form of Navier Stokes equation is (assuming $v,q$ test functions for the velocity and the pressure, respectively) $$(\frac{du}{dt},v)_{\Omega} + (\...

I want to plot the motion of a positive charge in a cylindrically symmetric magnetic field. I am assuming a cylinder around the z-axis, with the magnetic field going in clockwise direction. The B-...

I want to find out the aggregated euclidean distance of a big dataset $D$ comprising of x and y coordinates where the data set is divided into N sub dataset where 1st sub dataset contains 1 to k-th ...

We are finding in Python some occasional errors in our coordinate transforms and other similar computations that produce a result of -0.0. What purpose does this ...

My experiment involves 6 different groups (A...F) subjected to different concentrations of a compound for a period of time. I observed each group at 7 different points in time for 3 binary traits (&...

I am implementing a simulation that needs to rotate and object based on known angular velocity (assumed constant for simplicity). I followed the ideas given below, pg. 32) https://graphics.stanford....

I'm trying to perform a 4-dimensional numerical integration in R using a function I wrote in C++ code which is then sourced in <...

I have the element stiffness matrix for a thin "kirchhoff" plate. The plate is 3 [m] x 5 [m] and is simply supported on all edges. It's thickness is 0,2 [m]. On the plate there acts a ...

Here is the output of Numpy np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary Here is the output of Matlab ...

I have a system to simulate the bubble evolution at different temperature conditions. I used CVODE_DENSE algorithm to solve the ODEs and get the bubble size and ...

I am trying to solve this with odeint module. But the first equation is function of second equation. If i ignore dw/dz in first equation and second equation is function of first one. I can solve it ...

Suppose I rasterize a rectangle of width 2.5 gridpoints and get the values as shown: =============== | 0 | 1 | 1 | 0.5 | 0 | Now I resample that ...

I didn't really know if this stack was the right place to post but I was reading the documentation for creating an exponential random variable in numpy. But isn't there a typo. Like shouldn't it be : $...

Problem statement I implemented geometric multigrid for $-\nabla^{2}=f$ where $f=\frac{3\pi^{2}}{4}sin \frac{\pi x}{2} sin \frac{\pi y}{2} sin \frac{\pi z}{2}$ on $\Omega \in [0,1]$ on a unit cube. ...

I am working on implementation of AMR for my finite volume code. Let me use a 2-D mesh to describe my question. Starting with SINGLE initial cell (let the mesh refine level k = 0) as a root of a quad-...

I have several challenging non-convex global optimization problems to solve. Currently I use MATLAB's Optimization Toolbox (specifically, fmincon() with algorithm=<...

I have two 2D histograms, A and B, calculated from simulations by changing a single input parameter (alpha and beta set at "5" and "7", respectively). I want to calculate a third ...

In a software project that I'm working on, certain computations are vastly easier for dense low-rank matrices. Some problem instances involve dense low-rank matrices, but they're given to me in full, ...

I am writing a code that checks the orientation of a list of vertices (along with face connectivity) describing both convex and concave hexahedra. The face connectivity table stores the list of vertex ...

I am trying to find a laplacian of the function explicitly using the RBF-FD approach The function is sin(pi*x)*cos(pi*z/2) and its analytical solution of the ...

I don't know how to solve the optimization problem. Please suggest a theory or approach to solving the above optimization problem.

From the package scipy.sparse.linalg in Python, calling expm_multiply(X, v) allows you to compute the vector ...

During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in ...

I always see Finite Element codes solving PDE with Dirichlet or Neumann boundary conditions. But, I have a problem now consisting of a straight cylinder with a circular base (a simple 3D tube), with ...

I wanted to learn how to implement a code for the Stokes and Navier--Stokes equations 2D/3D. I already know how to implement it when the elements are triangles or tetrahedral. Do exists finite element ...

I am currently trying to get through Pattern Classification by Duda et al (for a course). However, the book seems too dense for me. Pattern recognition seems like a topic that could be better learned ...

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...

How to compute 2-norm or infinity norm of following system? i am confused whether to calculate using simple matrix theory "where it don't regard for s domain" or H2 and H-infinty norm. ...

I am trying to solve a system of PDEs $H_{t} = \frac{0.3}{0.7} - \frac{0.005 B f(h(H))}{\theta} - \frac{0.3 f(h(H))}{0.7} + \frac{500}{0.7} (HH_x)_x + (HH_y)_y$ $N_t = \frac{N_{in} - 0.002 [N] B f(h(...

I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...

I'm trying to debug an FEM that I inherited, and I unfortunately do not have much knowledge of FEM. I only know FD and FVM. If you're modeling a system with 2 materials, there will be an interface ...

I am working on a problem where I need to solve approximately 500 Million Linear Regressions (OLS). What would be the most efficient way to do this (e.g. using GPU or a some framework that can do this ...

When someone refers 2-norm of system,L2 and H2 are used interchangeably by author and is rather confusing. Even the matlab has different functions for H-infinity norm and L-infinity norm. as shown in ...

I am looking for FOSS code that can generate self-avoiding random walk trajectories on a tetrahedral lattice. The purpose of the exercise is to create random conformations of model polymer chains that ...

Consider the following PDE \begin{align} -\Delta u &= f \ \ \text{en} \ \ (0,1)\times (0,1) \label{P1} \\ u &= 0 \ \ \text{en} \ \partial ((0,1)\times (0,1)) \label{P2} \end{align} if we ...

I understand that the Arnoldi iteration produces a basis which tends to include in its span the eigenvectors corresponding to eigenvalues of large magnitude (hence the analogy between the last vector ...

The leap-frog algorithm is able to conserve to a certain extent the energy of a system, which flucutates as a cosine around a stable value. Is this true if we apply the algorithm to a n-body ...

I want to know the time complexity of following code Say I have a list unique_element[] There is an array which contain elements {4,5,2,4,7,8,1,5,9,8,1} Now as per my code I want to find out the ...

I calculate 2D Model of Magnetotelluric responses which are apparent resistivity and phase. I do the calculation for Transverse Electric (TE) mode. Then I used edge based finite element with ...

I have an ordinary differential equation that is solved as an initial value problem using different numerical schemes. I end up with several discrete time signals that should display a reasonably ...

The mixed form of the elasticity equations is to find the unique critical point of the Hellinger-Reissner functional $$J(u, \sigma) = \int_\Omega\left(\frac{1}{2}A\sigma : \sigma - (\nabla\cdot\sigma)\...

Consider the heat equation $$u_t = \kappa u_{xx}$$ with boundary conditions of $$u(x,0)=0\\ u(0,t)=100\\ u(l,t)=0$$ Numerical analysis by pyton can be done with ...