Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
Preconditioning the Poincaré-Steklov operator by using Green's function
Mathematics of Computation
Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure
SIAM Journal on Scientific Computing
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Convergence analysis of additive Schwarz for the Euler equations
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
SIAM Journal on Numerical Analysis
Optimized Schwarz Methods for Maxwell's Equations
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
In this paper, the tight relationship between Dirichlet-Neumann (D-N) operators and optimized Schwarz methods with Robin transmission conditions is disclosed. We describe the spectral distribution of continuous D-N operators and give a rigorous spectral analysis of discrete D-N operators. By these results, we prove that the optimized Schwarz methods with Robin transmission conditions cannot converge geometrically in the case of continuous problems. Furthermore, we get the accurate convergence rate of the two-subdomain case. In addition, an estimation of convergence rate of the optimized Schwarz methods is presented in the general case. Most of our results are asymptotically sharp.