# Questions tagged [multigrid]

Questions about multigrid methods for numerically solving differential equations.

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### Find the number of rectangles not containing the shaded square [closed]

I wish to find the number of rectangles that don't contain the shaded square: Image of the grid: I used the way of finding the total number of rectangles and subtracting the rectangles containing the ...
1 vote
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• 33
1 vote
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### How are interpolation operators derived for multigrid

I am trying to construct transfer operators $I^H_h, \, I^h_H$ for multigrid where $H \ne 2h$. I have gone through Briggs' tutorial, Hemker's paper, Hackbush's book, Trottenberg's book, but the details ...
• 2,047
1 vote
36 views

### Connection two-grid, multigrid and finite elements

In some literature for the two grid method the finite element method is given as an introduction to the topic. But why is it done that way and where is the connection between these methods? The finite ...
• 83
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### What does it mean that a laplacian of directed graph has full rank?

Suppose we have a directed graph $G=(V, E)$ with $N=|V|$ nodes. Define normalized graph laplacian as $L=I-AD^{-1}$ where $A$ is a adjacency matrix of $G$ and $D$ is a degree matrix of $G$. I'm ...
1 vote
38 views

### Quantization to minimize multiplicative error

Consider a random variable $X$ taking values in $[0, 1]$ with unknown distribution. Consider the set $S_n = \left \{\frac{1}{n}, \frac{2}{n}, ..., \frac{n-1}{n} \right \}$ to be used to quantize $X$. ...
• 2,657
323 views

### How is a matrix connected to a grid?

I have a hard time finding information about and understanding how a matrix (adjacency matrix) is connected to a grid used in numerical analysis. What would the nodes be and are the matrix weighted or ...
1 vote
31 views

• 111
1 vote
270 views

### - Optimization - Standard Grid Search

I'm struck into an portfolio opt. problem and the paper I'm replicating (or, better, trying to) is using a "Standard Grid Search". Since I never encountered it before, I would like to ask you about: ...
48 views

### Number of rectangle of size x,y which cover a cell p,q

I have a rectangle of size n*m (Where n is a number of rows and m is the number of columns) which is divided into of size 1*1. I want to calculate the number of the rectangle of size P*Q which ...
• 101
1 vote
182 views

### What does "smooth" mean? (Numerical Analysis)

I know a notion of smoothness for functions, say, in $\mathbb{R}^n$, which simply means of class $C^\infty$. But in studying Numerical Analysis I sometimes read the term smooth for discrete functions, ...
94 views

### Is the application of the multigrid method correct?

We consider the boundary problem \begin{align*}-&y''(x)=0 \ \ \text{ for } \ x\in \Omega:=(0,\pi) \\ &y(0)=y(\pi)=0\end{align*} Let's pick the grid size $n=5$. I want to apply the 2-grid ...
• 14k
1 vote
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### ADMM Heuristic or rather stick to Branch and Bound?

I'm intending on giving a solution to this MIQP, which should be faster than the one of solving the exact problem with GUROBI or CPLEX.(It muss not give always the global solution!) The main ...
• 21
1 vote
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### How many ways can blocks be arranged in a grid

I have a 16x16 grid to fill up with 4 different sized blocks listed below: 16x16 16x8 8x16 8x8 How many different combinations of 16x16 grids can I make while filing the grid up completely? Just to ...
• 143
1 vote
64 views

### Looks like a magic square, but can't solve it, please help.

A friend sent me this from her game I tried many combinations and I cannot solve it for the life of me. 9 squares starting from each corner is (top left 61, top right 61, bottom left 69, bottom ...
• 11
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### Finding the value of a point in 3D domain depending on neighboring points

I have some data on 3D models of soil's moisture content, the model is in the finite-element grid. I have converted the program outputs to a table in four columns x, y, z, Theta where Theta is the ...
63 views

### Can L, the square lattice on the plane, be partitioned into finitely many subsets that (up to translation) are contained in a rotated version of L?

I ran into this interesting problem while thinking about some stats models the other day. The context was efficient estimation of anisotropic covariance structures in geostatistical models, but it ...
1 vote
380 views

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### Addressing/traversing an infinite 2D grid using a Z-line?

I'm looking for a method to map an infinite 2D grid using a line, so that I would have just one integer from which I would compute the X and Y. I know something like that exists, but can't recall the ...
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