This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directio...

where Ω ⊂ R, with n = 2 for the results in section 4. Q and ∂Q are defined as Q ≡ Ω× (0, T ) and ∂Q ≡ ∂Ω× (0, T ), respectively. See [8] for details on system parameters. The objective of the parameter identification is to reconstruct the reactive coefficient α(x) in the first equation from boundary measurements of the electrical potential u. Our aim here is to present a numerical algorithm tha...

We present parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace methods for the numerical solution of stochastic elliptic problems, whose coefficients are assumed to be a random field with finite variance. Karhunen-Loève (KL) expansion and double orthogonal polynomials are used to reformulate the stochastic elliptic problem into a large number of related, but unco...

In this paper we present a domain decomposition method for the solution of a linear equation as a direct two-step procedure (in contrast to iterativebased Schwarz and Aitken-Schwarz procedures): first, local solutions to the nonhomogeneous equation are calculated on overlapping domains, and second, connection functions, solutions to the homogeneous equation, are calculated which satisfy the Cou...

Numerical solution of variational inequalities of obstacle type associated with second-order elliptic operators is considered. Iterative methods based on the domain decomposition approach are here proposed for discrete obstacle problems arising from the continuous, piecewise linear nite element approximation of the diierential problem. A new variant of the Schwarz methodology, called the two-le...

Closed strings spinning in AdS3 × S × T with mixed Ramond-Ramond and Neveu-Schwarz-NeveuSchwarz three-form fluxes are described by a deformation of the one-dimensional Neumann–Rosochatius integrable system. In this articlewe find general solutions to this system that can be expressed in terms of elliptic functions.We consider closed strings rotating either in S with two different angular moment...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 16 December 2020Accepted: 25 June 2021Published online: 05 October 2021Keywordsadditive Schwarz methods, adaptive coarse spaces, heterogeneous coefficientsAMS Subject Headings00A20Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Indust...

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...