All Questions

9,959 questions
Filter by
Sorted by
Tagged with
37 views

Find alternative path closest to original

I have a set of points in a 2D space. I want to connect the outer points so I get the convex hull. The problem here is that there is a limit to the distance between two points. Let me clarify that ...
82 views

A linear polynomial that is the minimax (best) approximation to $f(x)$ on the interval $[-1,1]$

Suppose you have the following analytical information about a function $f(x)$ on $[-1,1]$: \begin{align*} f(x) &= \frac{1}{x+3}\\ f'(x) & = -\frac{1}{(x+3)^2}\\ f^{''}(x) &= \frac{2}{(x+3)...
42 views

Formation sketching; trouble with sampling unit optimization

I'm looking for assistance in understanding a concise portion of a paper that involves a quadratic equation, so that I can properly implement it. There are 2 versions of the paper. Each paper ...
129 views

133 views

Generate gaussian random field in spherical polar coordinates

I would like to generate an isotropic gaussian random field described by a power spectrum $P(k)$ on a 3D grid which represents spherical polar coordinates (i.e., the angular separation between pixels ...
558 views

Rank sufficiency concept in Finite Element

From section 19.4.1, Rank Sufficiency: The element stiffness matrix must not possess any zero-energy kinematic mode other than rigid body modes. This can be mathematically express as follows....
656 views

Seismic Wave modelling: Elastic Wave or Acoustic Wave?

I am modelling a seismic wave equation using FEM. In the few papers that I read, I understand the following: (Kindly correct me if you disagree) A shear (secondary wave - no change of volume) is more ...
147 views

Updating factorization of Laplacian (add/remove edges)

For a graph $G=(V,E)$, recall that the unweighted Laplacian is $L:=D^\top D$, where $D\in\{-1,0,1\}^{|E|\times|V|}$ is the graph "gradient" operator that subtracts adjacent vertex values onto edges. ...
171 views

97 views

What is meant by "operations"?

In this paper, on page 243, we have $$d_{jk} = \frac{a_j}{a_k(x_j - x_k)}$$ where $$a_k = \prod_{l = 0;l\neq k}^{N}(x_k-x_l)$$ Now, $a_k$ requires evaluating N multiplications. Why does the author ...
84 views

RNG float range for metropolis monte carlo

I have a robust RNG that generates random 32-bit (unsigned) ints. As is probably well known, for metropolis MC simulation, a random number between 0 and 1 is needed to determine acceptance/rejection ...
71 views

360 views

Solving system of constrained linear and non-linear equations in MATLAB

Solving system of constrained linear and non-linear equations in MATLAB I'm solving a FEM problem in MATLAB with use of the direct stiffness method. The problem is now formulated as a system of nn ...
76 views

Manufacturing a solution for non-smooth coefficients in elliptic problems

This question is a continuation of this answer (I can't comment) If we were going to manufacture a solution for a problem with discontinuous coefficients, I understand that the solution should have ...
199 views

How to make objective elastic SPH model?

I have implemented a constitutive equation of elastic materials (Hooke's law) in my 3D weakly compressible SPH solver based on [1]. The coding seems to be correct. To verify the implementation I ...
607 views

Issues with self-consistent Poisson-Schrodinger solver

I'm currently in the process of writing a self-consistent Schrodinger-Poisson solver for a device heterstructure (High Mobility Electron Transistor). The algorithm is based off of this journal(1). I ...
64 views

How to make the following data separable for the classification into three classes?

The figure below shows the PCA projections of inputs which are 14 meteorological features, (i.e. wind, temperature, humidity, pressure, and so on.) I would like to use any technique to make it more ...

15 30 50 per page