A fast two-grid method for matrix H-equations

Abstract

We present a new two-grid method for solution of matrix H-equations that is a generalization of a method due to Atkinson. Our new algorithm provides mesh independent q-linear convergence and can be accelerated to a superlinearly convergent algorithm by means of a quasi-Newton method. In addition the algorithm requires far less storage than Newton's method. Such considerations are especially important for the large problems generated by discretizations of H-equations for matrix-valued functions. Such equations arise in radiative transfer, polarization, and multi-group neutron transport. As a numerical example we show measured convergence rates and discuss timings for a matrix H-equation arising in radiative transfer.