Questions about multigrid methods for numerically solving differential equations.

learn more… | top users | synonyms

0
votes
0answers
37 views

Transform cos to e function

What are the steps in order to transform the cosine function to the exponential function: $$ \left[\cos \left(\frac{k \pi} N\right)\right]^n \approx e ^ {\frac{-n}2 \left(\frac{k \pi} N \right)^2} ...
0
votes
0answers
21 views

Multigrid for power of two number of grid points

Until now I have written a C++ geometric multigrid code for solving problems with number of grid points of the kind 2^l+1. For these problems the spatial step size is one over an even number. This ...
0
votes
0answers
26 views

One Million Proficiency Efficiency Calculations

I have been playing the "Million" game on my apple device after discovering it through the trending applications in the search function. After beating the game I began to wonder to myself if there was ...
0
votes
1answer
92 views

How to make Galerkin coarse operator in multigrid?

In multigrid, the coarse operator is given by $$A^{2h}=RA^hP$$ where $R$ is a restriction and $P$ is a interpolation. In 1D case, I can implement it easily with or without making explicitly matrix ...
0
votes
1answer
26 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 $k \times 1$ ...
0
votes
1answer
51 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 ...
1
vote
2answers
281 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 ...
0
votes
1answer
44 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 $(x,y)$ ...
1
vote
0answers
21 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 ...
1
vote
0answers
578 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[ ...
0
votes
0answers
49 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 ...
1
vote
1answer
174 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 ...