Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions | Zendy

ShuLin Wu | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Schwarz Waveform Relaxation for Heat Equations with Nonlinear Dynamical Boundary Conditions

Author(s) -

ShuLin Wu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/474608

Subject(s) - mathematics , nonlinear system , relaxation (psychology) , schwarz alternating method , domain decomposition methods , waveform , convergence (economics) , mathematical analysis , boundary value problem , rate of convergence , heat equation , additive schwarz method , boundary (topology) , spacetime , sequence (biology) , computer science , finite element method , physics , psychology , social psychology , telecommunications , radar , channel (broadcasting) , computer network , genetics , quantum mechanics , biology , economics , thermodynamics , economic growth

We are interested in solving heat equations with nonlinear dynamical boundary conditions by using domain decomposition methods. In the classical framework, one first discretizes the time direction and then solves a sequence of state steady problems by the domain decomposition method. In this paper, we consider the heat equations at spacetime continuous level and study a Schwarz waveform relaxation algorithm for parallel computation purpose. We prove the linear convergence of the algorithm on long time intervals and show how the convergence rate depends on the size of overlap and the nonlinearity of the nonlinear boundary functions. Numerical experiments are presented to verify our theoretical conclusions

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research