Schwarz methods are attractive parallel solvers for large-scale linear systems obtained when partial differential equations are discretized. For hybridizable discontinuous Galerkin (HDG) methods, this is a relatively new field of research, because HDG methods impose continuity across elements using a Robin condition, while classical Schwarz solvers use Dirichlet transmission conditions. Robin c...

We investigate the performance of domain decomposition methods for solving the Poisson equation on the surface of the sphere. This equation arises in a global weather model as a consequence of an implicit time discretization. We consider two different types of algorithms: the Dirichlet-Neumann algorithm and the optimal Schwarz method. We show that both algorithms applied to a simple two subdoma...

We demonstrate that a small modification of the multiplicative, additive and restricted additive Schwarz preconditioner at the algebraic level, motivated by optimized Schwarz methods defined at the continuous level, leads to a significant reduction in the iteration count of the iterative solver. Numerical experiments using finite difference and spectral element discretiza-tions of the positive ...

We investigate how the mass correction appears in 5-D with Scherk-Schwarz compactification and clarify whether the KK regularization is reliable method or not. In the extremely sharp cutoff limit of the 5-D regulator which preserves 5-D Lorentz invariance, we prove that the one loop correction to the mass does not depend on the ultraviolet physics for the Scherk-Schwarz breaking of supersymmetr...

Domain decomposition algorithms based on the Schwarz alternating method are developed for the numerical solution of singularly perturbed semi-linear elliptic problems. The emphasis is given to the description of two variants of the algorithm (multi-domain Schwarz alternating method and two-level Schwarz method) as well as their computer realization on a distributed memory multi-processor comput...

A Schwarz Waveform Relaxation (SWR) algorithm is proposed to solve by Domain Decomposition Method (DDM) linear and nonlinear Schrödinger equations. The symbols of the transparent fractional transmission operators involved in Optimized Schwarz Waveform Relaxation (OSWR) algorithms are approximated by low order Lagrange polynomials to derive Lagrange-Schwarz Waveform Relaxation (LSWR) algorithms ...

The paper is devoted to the numerical solution of both elliptic and parabolic problems by overlapping Schwarz methods. It demonstrates that while the two-level Schwarz method is necessary for the efficient solution of discrete elliptic problems, the one-level Schwarz method can be sufficiently efficient in the parabolic case. The paper includes results from numerical simulations of a large-scal...