Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, using characteristic transmission conditions, and it has been observed that the classical Schwarz method can be convergent even without overlap in certain cases. This is in strong contrast to the behavior of classical Schwarz methods applied to elliptic problems, for ...

In this paper we consider a Dirichlet problem for singularly perturbed ordinary differential equations with convection terms and a small perturbation parameter ε. To solve the problem numerically we use an ε-uniformly convergent difference scheme (on special piecewise-uniform meshes) and a decomposition of this scheme based on a Schwarz technique with overlapping subdomains. The step-size of su...

The Additive Schwarz Method with Harmonic Extension (ASH) was introduced by Cai and Sarkis (1999) as an efficient variant of the additive Schwarz method that converges faster and requires less communication. We show how ASH, which is defined at the matrix level, can be reformulated as an iteration that bears a close resemblance to the parallel Schwarz method at the continuous level, provided th...

A Schwarz-type domain decomposition method is presented for the solution of the system of 3d time-harmonic Maxwell equations. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of the problem based on a tetrahedrization of the computational domain. The discrete system of the HDG method on each subdomain is solved by an optimized sparse direct (LU factorizatio...

and Applied Analysis 3 Let us turn to the positivity of Δ. Given vector f = (f 1 ,

Abstract In this article, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as counterpart classical framework problem A key ingredient is special anisotropic gauge, which enables us to transform convex introduced Alvino et al. https:/doi.org/10.1016/S0294-1449(97)80147-3 .

As epitomized by Blaise Pascal's famous quote, "The heart has its reason of which reason knows nothing," emotions have historically been conceived as psychobiological forces that energize and channel people's behavior, sometimes at the expense of their better judgment. In advancing the "affect-asinformation" hypothesis that moods, feelings, and emotions serve as sources of information, Schwarz ...

We prove a partial result concerning the long–standing problem on limit periodicity of the Jacobi matrix associated with the balanced measure on the Julia set of an expending polynomial. Besides this, connections of the problem with the Faybusovich–Gekhtman flow and many other objects (the Hilbert transform, the Schwarz derivative, the Ruelle and Laplace operators) that, we sure, are of indepen...

Under classical assumptions on the coefficients of the problem (e.g. η − 1 2divb > 0 a.e. in Ω) the matrix A in (2) is definite positive. We solve problem (2) by means of an Optimized Schwarz Method: such methods have been introduced at the continuous level in [4], and at the discrete level in [5]. We design optimized interface conditions directly at the algebraic level, in order to guarantee r...