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 ...

In this paper, we present a global-in-time non-overlapping Schwarz method applied to the Ekman boundary layer problem. Such coupled problem is representative of large-scale atmospheric and oceanic flows in vicinity air-sea interface. waveform relaxation (SWR) algorithms provide attractive methods for ensuring “tight coupling” between ocean atmosphere. However, convergence study such context rai...

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposi...

Thanks to powerful algorithms and computers, Schwarz{ Christooel mapping is a practical reality. With the ability to compute have come new mathematical ideas. The state of the art is surveyed. 1. Introduction. In the past twenty years, because of new algorithms and new computers, Schwarz{Christooel conformal mapping of polygons has matured to a technology that can be used at the touch of a butt...

The scalability of a fully implicit global shallow water solver is studied in this paper. In the solver a conservative second-order finite volume scheme is used to discretize the shallow water equations on a cubed-sphere mesh which is free of pole-singularities. Instead of using the popular explicit or semi-implicit methods in climate modeling, we employ a fully implicit method so that the rest...

The convergence rates and, therefore, the overall parallel efficiencies of additive Schwarz methods are often notoriously dependent on subdomain granularity. Except when effective coarse-grid operators and intergrid transfer operators are known, so that optimal multilevel preconditioners can be constructed, the number of iterations to convergence and the communication overhead per iteration ten...

The Schwarz Alternating Method is a method devised by H. A. Schwarz more than one hundred years ago to solve linear boundary value problems. It has garnered interest recently because of its potential as a very efficient algorithm for parallel computers. See the fundamental work of Lions in [7] and [8]. The literature on this method for the boundary value problem is huge, see the recent reviews ...

We developed parallel time domain decomposition methods to solve systems of linear ordinary differential equations (ODEs) based on the Aitken-Schwarz [5] or primal Schur complement domain decomposition methods [4]. The methods require the transformation of the initial value problem in time defined on ]0,T ] into a time boundary values problem. Let f (t,y(t)) be a function belonging to C 1(R+,Rd...