Numerical efficiency of modified modulus-based multigrid cycles with application to free boundary problems

Abstract

When the modified modulus-based multigrid method is applied to solve free boundary problems, the V-cycle does not show a grid-independence convergence rate. To improve the convergence rate of the V-cycle, we consider a modified V-cycle which is a combination of the V-cycle on coarser grids and the W-cycle on finer grids. We also consider the F-cycle. The computational works of these multigrid cycles are given to show their numerical efficiency. Numerical results show that both the modified V-cycle and the F-cycle can achieve the grid-independence convergence rate compared with the V-cycle and can reduce the computing time compared with the W-cycle.