Kernel approximation of a function ↩

Metadata

aliases: []
shorthands: {}
created: 2022-04-24 22:52:51
modified: 2022-04-24 23:18:05

In the kernel approximation, we represent a function and its derivatives using a smoothing function.

The kernel approximation of is:

Where is the smoothing function, is the domain of and is the smoothing length defining the influence or support area of the smoothing function .

Comments

When we choose the Dirac delta function as , then we get an exact representation
The smoothing function is usually chosen to be an even function
The smoothing function also have to satisfy a number of conditions (See Smoothing kernel)
It has second order accuracy: