Monotone enclosure for nonlinear PDEs using multigrid techniques

摘要

Two possibilities to include numerical solutions of weakly nonlinear elliptic boundary value problems are considered. If one single equation is given, it is usually more efficient to solve it by nonlinear multigrid methods than to linearize it and to use a linear multigrid algorithm afterwards. To get a monotone-including nonlinear multigrid method, we present a modified FAS called MMG3. If a weakly coupled system of equations is given, it is sometimes more convenient to linearize it with a conventional monotone iteration method and to use a linear multigrid algorithm as inner iteration. This is demonstrated here by considering Volterra- Lotka systems with diffusion.