In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a forward parabolic system, an adjoint system and a system with respect to the unknown sources. The three systems have to be solved one after another. These seque...

In this work we consider the Optimized Schwarz Method for the three-dimensional (3D) diffusion-reaction problem. In particular, we treat the case of cylindrical interfaces between the subdomains, and we provide for such case a convergence analysis of the Schwarz method, both in the case of Dirichlet interface conditions and in that of general transmission conditions. This allows to recover, for...

The problem of gravitation near the Schwarzschild radius is addressed. pressure due to free fall velocity introduced. At Schwarz-schild radius, this produces force balancing gravity thus stopping collapse matter. minimum source defined as a at which proton reaches Planck energy. compact object thin shell considered. assumed decay scale into positron and hypothetical neutrinos. Under accretion o...

We compare additive and multiplicative Schwarz preconditioners for the iterative solution of regularized linear inverse problems, extending and complementing earlier results of Hackbusch, King, and Rieder. Our main ndings are that the classical convergence estimates are not useful in this context: rather, we observe that for regularized ill-posed problems with relevant parameter values the addi...

The aim of this paper is to establish some properties solutions the Dirichlet–Neumann problem: $$(\partial _z\partial _{\overline{z}})^2 w=g$$ in unit disc $${{\mathbb {D}}}$$ , $$w=\gamma _0$$ and $$\partial _{\nu }\partial _{\overline{z}}w=\gamma $$ on $${\mathbb {T}}$$ (the circle), $$\frac{1}{2\pi i}\int _{{\mathbb {T}}}w_{\zeta {\overline{\zeta }}}(\zeta )\frac{d\zeta }{\zeta }=c$$ where _...

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...

In this paper we generalize the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation for parabolic problems. The domain decomposition is in space and time. The standard Schwarz waveform relaxation algorithm has a linear rate of convergence and low numerical efficiency. This algorithm is, however, friendly to cache us...

The purpose of this paper is to provide two numerical methods for solving the elastic body-plate problem by nonoverlapping domain decomposition type techniques, based on the discretization method by Wang. The first one is similar to an older method, but here the corresponding Schur complement matrix is preconditioned by a specific preconditioner associated with the plate problem. The second one...