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Multigrid Implementation in COMSOL Multiphysics® - Comparison of Theory and Practice

W. Joppich[1]
[1]University of Applied Sciences, Sankt Augustin, Germany

Multigrid methods (MG) belong to the fastest solvers for partial differential equations. The key for this is an appropriate composition of the algorithmic components [1,2,4]. The multigrid solver implemented in COMSOL Multiphysics® is analyzed with respect to components and with respect to its numerical properties. Of special interest is the question whether solving selected model problems shows that behavior which is known from multigrid theory.

COMSOL Multiphysics® allows the composition of time-, convergence-, and memory-efficient MG algorithms both for model problems and concrete applications which work in the range predicted by theory and known by experience.