Conjugate gradient boundary iterations: a parallelization method for elliptic partial differential equations with applications to flow problems

S. Kräutle, University of Erlangen, Germany

Wednesday, January 8
at 16.30
in HG E1.1

CGBI (the Conjugate Gradient Boundary Iteration) is a parallelization method based on domain decomposition. It enables the coupling of different local solvers, e.g., unite element (FE) and Chebyshev spectral (CS) solvers, CGBI consists of a preconditioned conjugate gradient iteration acting on the subdomain interfaces only; in each iteration step, the local solvers on the sub-domains are called once. The preconditioning for CGBI does not require the timeconsuming solution of any kind of subdomain problem. Nevertheless, for channel-like geometries, it can be shown that the convergence rate is independent on the channel length and on the discretization parameter. Typical CGBI convergence rates are 1-2 powers of ten per iteration step. Based on CGBI a Navier-Stokes solver for channel-like domains was developed, After expounding CGBI and some theoretical results, numerical results for the solution of the Poisson resolvent equation on a channel-like domain and for the Navier-Stokes solver based on CGBI and FE-CS coupling are presented (2D-now past a cylinder in a channel, 2D-flow past a backward facing step).