Question

Let r^k be the residual in the k^th level of multi-grid approach. Which of these give the restriction operator?

(a) \(\frac{r^{k+1}}{r^k} \)

(b) \(\frac{r^k}{r^{k+1}}\)

(c) r^k+1-r^k

(d) r^k-r^k+1

I have been asked this question during an internship interview.

My doubt is from Numerical Methods topic in division Numerical Methods of Computational Fluid Dynamics

Answer 1

Right answer is (a) \(\frac{r^{k+1}}{r^k} \)

The best I can explain: The first step in the multi-grid approach is the restriction step. Here, the process starts with a fine grid. After a few iterations, the error is transferred to a coarser grid level. Again, some iterations are performed in that step and the process continues. The restriction operator for the error transferred from one step to the higher step is \(\frac{r^{k+1}}{r^k} \).