We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in ratio between subdomains overlap sizes. Our validated through a set of numerical experiments illustrate good behavior proposed with respect to model param...

In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known method...

We propose a new two-level nonlinear additive Schwarz preconditioned inexact Newton algorithm (ASPIN). The two-level nonlinear preconditioner combines a local nonlinear additive Schwarz preconditioner and a global linear coarse preconditioner. Our parallel numerical results based on a lid-driven cavity incompressible flow problem show that the new two-level ASPIN is nearly scalable with respect...

SUMMARY A preconditioning theory for Schwarz methods is presented. The theory establishes suucient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive deenite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition...

We establish sufficient conditions for the unique solvability of inverse problem finding two unknown functions from a Schwarz-type space smooth rapidly decreasing at infinity on right-hand side diffusion equation with Caputo–Djrbashian time fractional derivative. In this case, we use overdetermination integral respect to time.

A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and ...

Various variants of Schwarz methods for a singularly perturbed two dimensional stationary convection-diffusion problem are constructed and analysed. The iteration counts, the errors in the discrete solutions and the convergence behaviour of the numerical solutions are analysed in terms of their dependence on the singular perturbation parameter of the Schwarz methods. Conditions for the methods ...

Numerical conformal mapping techniques can be roughly divided into two categories. On one hand there are many methods which perform well on regions with smooth boundaries , but which either fail or require elaborate modiications when mapping regions with corners. On the other hand there is the Schwarz-Christooel transformation, which is speciically designed for mapping polygons with any number ...

Homographic complex best approximation has emerged in recent years as an essential tool for the design of new, performant domain decomposition Robin--Schwarz algorithms. We present and analyze a fully problem, introducing new alternation property. give operational formulas solution apply them to control problem.