# All Questions

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### How to evaluate the average value of a polynomial inside the triangle area in finite volume sense?

Consider we have a linear bivariate polynomial: $$p(x,y)=ax+by+c.$$ To construct the linear polynomial using least square method, we need to evaluate the value of the average polynomial $p$ in at ...
24 views

### Mesh transition between beam and shell element types

I am using NASTRAN solver & FEMAP as preprocessor for reduce modelling of wing using 1D and 2D finite elements. Beside transition of 1D & 2D elements to 3D, I had not found any method/solution ...
62 views

### How are the classical set of equilibrium equations for linear elasticity derived?

In linear elasticity, the governing PDE is the equilibrium equations (absent of vibration considerations): $$-\nabla \cdot \sigma = F$$ Is this equation simply derived from the sum of forces and ...
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### 'Eigen' matrices with static dimension

I noticed that 'Eigen' matrices with dynamic dimension are less efficient than the matrices with static dimension. My algorithm uses a lot of matrices which don't need to be resized, so I wanted to ...
54 views

### Cauchy Lorentzian simulation on FFT with oscillation

Recently I do simulation on Lorentzian Function with FFT Lorentzian Function is 2a/(x**2+a**2) ...
14 views

### how to compute the computational complexity of cellular neural networks?

Anyone, please help us that how to compute the computational complexity of the dynamic state of the single-cell and total cells for the 2D-CNN (two-dimensional cellular neural network). 2D-CNN of M * ...
100 views

### Create a sparse matrix

I am writing a FE program which calculates the displacements under a uniform load. I want to store the stiffness matrix in sparse form(COO) without using an external library.Assume an upper-bound for ...
44 views

### How can I color my Mandelbrot set like this?

I have a background image of a fractal on my phone that I would like in a higher resolution with super sampling, and decided to write my own program for it. I've got down rendering a Mandelbrot set, ...
13 views

### Minimal covering of rectangle with fixed, overlapping rectangles

A finite set $R$ of fixed, axis aligned 2-D rectangles $r_i=\left\{x_{0i},y_{0i},W_i,H_i \right\}$ is given. These rectangles are potentially overlapping. Given a new axis aligned rectangle $t$, I ...
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### Iterative single variable solutions in large linear systems

I have a system where $A$ is a large $n\times n$ marix with fast MVMs. It may have many nonzero entries (albeit in a structured way so as to allow fast MVMs), and is not necessarily diagonally ...
97 views

### Solving $AX+X^TB=C$?

Is there a name/standard algorithm to solve the following equation for $X$? $AX+X^TB=C$ Matrices $A$,$B$,$C$ are dense, diagonalizable, nearly singular, about $1000\times 1000$ in size. I've looked ...
45 views