Two-Level Method on Unstructured Meshes with Convergence Rate Independent of the Coarse-Space Size
Petr Vaněk, Jitka Křížková · 1995
. A two-level algorithm for unstructured meshes with a coarse-space size independent rate of convergence is developed based on polynomial smoothing of prolongators given by unknowns aggregation. A coarse level is generated algebraically using a system of possibly large subdomains. Numerical experiments confirm the theory and demonstrate that the method performs well also on a general class of problems with highly variable coefficients. Key words. Unstructured meshes, two-level method, coarse-space size independent rate of convergence. AMS(MOS) subject classifications. 65N55, 65F10 1. Introduction. When solving iteratively a large system of linear equations obtained by discretization of an elliptic boundary value problem, one needs to establish a mechanism of global distribution of information in order to supress the low energy components of the error. In the case of multilevel methods, this effect is achieved by creating a system of nested coarse spaces and combining the exact solut...