A Robust Domain Decomposition Method for General Symmetric Positive Definite Operators

Dr. Jörg Willems

July 26, 2010, 11 a.m. HF 136

We consider the preconditioning of symmetric positive definite operators. These operators for example arise in the discretization of PDEs modeling porous media flow, heat conduction, and many other processes. For preconditioning we apply a two-level additive Schwarz preconditioner, whose coarse space is constructed by eigenfunctions solving sets of suitably chosen (local) generalized eigenproblems. Due to this special choice of the coarse space the condition number of the preconditioned system is robust with respect to the mesh parameters and problem parameters such as variations in the permeability field in porous media flow.