Questions about multigrid methods for numerically solving differential equations.

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39 views

12 column grid, how to calculate for columns(5,7,8,9,10,11)?

I am terrible at math, this is css/sass related, but it's mainly a math question. I feel like the answer is very easy. You can see for example col-1 is ...
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0answers
17 views

Numerical Overflow in Dirichlet Boundary Value Problem On High Dimensional State

I am using multigrid methods to solve a quasilinear parabolic pde with Dirichlet boundaries. The problem is too long to reproduce here, but my question is more practical than theoretical: The state ...
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0answers
355 views

Multigrid Interpolation and Restriction operators

I have a question about the restriction and the interpolation operators of a Multigrid algorithm. Let those be given: The full weighting restriction stencil (in 2D): $\frac{1}{16} \left[ ...
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1answer
18 views

Plot my own function 'in two variables'

I have matlab function in two variables say $function_{something}(t)$ where $t$ is of size $2 \times k$, this is to allow to evaluate $k$ times in two values. So my output is then a $k \times 1$ ...
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1answer
34 views

A mathematical expression for “grid search”?

I've got a question whether there is a mathematical expression for a grid search? I have two parameters a and b in [0;1]. Depending on the values of a and b, I get a value for my function (the value ...
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1answer
37 views

What is it called when we interpolate a point INTO a grid…

Consider a uniform 2D grid, where each $(x,y)$ value on this grid has a corresponding value. So, if I want to find the value, $v$ (unknown) of a point that exists at some arbitrary co-ordinate $(x,y)$ ...
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0answers
18 views

Numbering Elements of Quadrilateral Mesh

I am having a Regular Structured Quadrilateral Mesh of size = $A \times B \times C$. The ID of the grids starts from $s$, that means $(0,0,0)$ will be $s$ and $(0,0,1)$ will be $s+1$. Now, I am ...
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0answers
18 views

Calculating h-ellipticity

How do we calculate h-ellipticity $E_{h}$ of standard five point discrete Laplacian of two dimensional partial differential equation?
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Isoparametric mapping

I have a some points and I want to map it to another shape (shown in picture). Can anybody explain me how to do it step by step and how many known points coordinate from the mapped shape do I need to ...
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0answers
40 views

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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1answer
131 views

Multigrid tutorial/book

I was reading Press et. al., "Numerical Recipes" book, which contain section about multigrid method for numerically solving boundary value problems. However, the chapter is quite brief and I would ...