Question

The cost of computing the Fourier coefficients is ___________ (Note: ‘N’ is the number of grid points).

(a) N^3

(b) N^2

(c) \(\frac{N^2}{2} \)

(d) \(\frac{N^3}{3} \)

I got this question in final exam.

Enquiry is from Finite Difference Methods topic in section Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Correct answer is (b) N^2

Easiest explanation: The computational cost required for computing Fourier coefficients, if done in the most obvious manner, is N^2. This is prohibitively expensive. It is twice that of the backward substitution for Gauss-Elimination method.