A Preconditioned Iterative Solution Scheme for Nonlinear Parabolic Systems Arising in Air Pollution Modeling

Abstract

A preconditioned iterative solution method is presented for nonlinear parabolic transport systems. The ingredients are implicit Euler discretization in time and finite element discretization in space, then an outer-inner (outer damped inexact Newton method with inner preconditioned conjugate gradient) iteration, further, as a main part, preconditioning via an l-tuple of independent elliptic operators. Numerical results show that the suggested method works properly for a test problem in air pollution modeling.

Keywords:

• nonlinear parabolic transport systems
• Newton's method
• inner-outer iteration
• air pollution models

AMS Subject Classification:

• 65F10
• 65M22
• 65M60