On the computation of axisymmetric electromagnetic fields

V.P. Il`in

Institute of numerical mathematics and mathematical geophysics, SD RAS,

Novosibirsk, e–mail:ilin@comcen.nsk.su

Abstract

On advanced numerical methods for the solution of equation

are considered. Here are piece-wise smooth functions, are corresponded to Poisson equation in Cartesian and cylindrical coordinates, and case describes axisymmetric magnetostatic field. High order compact finite difference nine-point schemes at the uniform rectangular grid are proposed. It`s generalization for nonuniform grids are investigated on the base of finite volume (balanced) approximations.

The modern fast iterative incomplete factorization methods for the solution of linear algebraic systems with very large sparse matrices are observed. An efficient convergence rate for the set of explicit and implicit algorithms is provided by generalized compensation approach, adapted meshordering and preconditioned conjugate gradient acceleration.

The results of numerical experiments demonstrate the fourth order accuracy of compact approximations as well as the robustness of proposed iterative procedures.