Fourier representation of intergrid operator for 2D scalar problem in multigrid method

摘要

A novel methodology for deriving Fourier representations of intergrid operators for 2D scalar problem is investigated with the help of local Fourier analysis (LFA) in multigrid methods. The objective was focused on intergrid operators: full weighting operator and bilinear interpolation. As a key starting point of the problems under consideration, the mathematical constitutions among Fourier modes with various frequencies was constructed as a base to develop Fourier representation of intergrid operators with respect to 2h-harmonics. Through the constitutions, the Fourier representation of full weighting operator and bilinear interpolation is given by means of LFA.