A parallel Schwarz preconditioner for the Chebyshev GaussLobatto collocation ( d 2 d x 2 ? h 2 ) operator
A Schwarz method is proposed to solve a Chebyshev one-dimensional Helmholtz problem of polynomial order k?n k ? n by iteratively solving problems of polynomial order up to n, which allows the use of a parallel algorithm. Its efficiency is commented. A multigrid global approach is implemented to accelerate the convergence, leading to an additive system of size 2k or 3k to be solved, depending on the kind of used boundary conditions. A preliminary application to a 2D problem is proposed.
schwarz methods chebyshev approximation preconditioning domain decomposition multigrid methods