A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh sizes and the number of subdomains, which proves the proposed preconditioner is optimal. Numerical results are provided to support the theoretical findings.
|Number of pages||18|
|Journal||Journal of Computational and Applied Mathematics|
|Early online date||2 Mar 2017|
|Publication status||Published - Sept 2017|