Algorithm for homogenization of non-equidistant 1-D grid

3 visualizaciones (últimos 30 días)
Michal
Michal el 1 de Dic. de 2021
Editada: Michal el 1 de Dic. de 2021
I am looking for proper algorithm for so called "delta-homogenization" of 1-D non-equidistant grid.
Definition: The sorted monotonically changing vector x is delta-homogeneous if for specified , the differences ratio
satisfy to the condition:
, for , where
Problem: In a case of non delta-homogeneous vector x, how to find minimum number of additional points , to be vector delta-homogeneous?
The problem is motivaded by proper design of non-equidistant grids, which are able to guarantee numerical stability of PDEs solution.
Example:
> x = (1:4).*(1:4)
1 4 9 16
>d = 1.5;
ratioviolationIdx =
1×2 logical array
0 1
ratios =
1.6667 1.4000
deltalimits =
0.6667 1.5000
So, x is not delta-homogeneous for delta = 1.5. But , the x is delta-homogeneous for delta = 2
>> [~,ratioviolationIdx,ratios,deltalimits] = isdeltahomog([x],2)
ratioviolationIdx =
1×2 logical array
1 1
ratios =
1.6667 1.4000
deltalimits =
0.5000 2.0000
An finaly, when I add several points to the vector x for delta = 1.5, I have delta-homogeneous vector
>> [~,ratioviolationIdx,ratios,deltalimits] = isdeltahomog([x 2.5 6 12],1.5)
ratioviolationIdx =
1×5 logical array
1 1 1 1 1
ratios =
1.0000 1.3333 1.5000 1.0000 1.3333
deltalimits =
0.6667 1.5000
See attached code...
Thanks in advance for any help.

Respuestas (0)

Productos


Versión

R2021b

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by