2
$\begingroup$

I have a solution of a 1D wave on a grid (tangent hyperbolic variation) and now I want to interpolate the obtained solution to a new grid with the same number of points as the previous grid but the domain length may or may not change. What are good techniques to do so? I read about Lagrange interpolation, Hermite interpolation etc. Are there any new better techniques to do so for interpolation of 1D solution?

$\endgroup$
2
  • 1
    $\begingroup$ The choice of method depends on the features of the interpolated function, and to some extent on the features of the grids. For example, if you want to remap a Heaviside step function to a new grid then using trigonometric high-order interpolation would not work well. But if your function is something like a smooth, well-resolved Gaussian then a high-order method should be good. $\endgroup$ Aug 27, 2022 at 17:21
  • 2
    $\begingroup$ Spline interpolation is hard to beat if you don't have any information about how the original function is supposed to look like between two nodes. $\endgroup$ Aug 27, 2022 at 20:11

1 Answer 1

4
$\begingroup$

A "better technique" is rather subjective. You mean faster, more accurate, easier to program, something else??

Since it's only 1-D, the numerical cost is small (compared to 2D/3D) and there are many algorithms available. I would suggest you to try the available algorithms and judge for yourself.

For similar cases, I have had great results using Gaussian Process Regression (in your case, since it's a wave I would try a cos() kernel), but if you want a more conventional approach look into PCHIP interpolation, this one has the nice property of keeping the monotonicity of the original data, so it should give a good representation of your wave.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.