Analysis of a Multigrid Method for a Transport Equation by Numerical Fourier Analysis

. In this paper, we perform Fourier analysis for a multigrid method with two-cell ¯-line relaxation for solving isotropic transport equations. Our numerical results show that the Fourier analysis prediction for convergence rates is more accurate than that previously found by matrix analysis. Keywords. Fourier analysis, multigrid, transport equations. 1. Introduction In this paper, we develop a Fourier analysis for a multigrid method which solves the isotropic transport equation in slab geometry given by ¯ @/ @x (x; ¯) + oe t /(x; ¯) = 1 2 oe s Z 1 \Gamma1 /(x; ¯ 0 )d¯ 0 + q(x; ¯); x 2 (0; 1); ¯ 2 [\Gamma1; 1]; (1) where /(x; ¯) represents the flux of particles at position x traveling at an angle ` = arccos(¯) from the x-axis, oe t is the macroscopic total cross section, q(x; ¯) is an external source. In what follows, we shall omit the external source term q for simplicity. The boundary conditions for equation (1) are given by /(0; ¯) = g 0 (¯); /(1; \Gamma¯) = g 1 (¯); ¯ 2 (0..